D6(1):S3
order := 6,
length := 60480,
subgroup := MatrixGroup(9, Integer Ring) of order 2 * 3
Generators:
[ 3 1 1 0 1 0 2 1 0]
[-1 -1 0 0 0 0 -1 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[-1 0 -1 0 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 5 3 1 2 2 1 1 2 0]
[-2 -1 0 -1 -1 0 -1 -1 0]
[-3 -2 -1 -1 -1 -1 -1 -1 0]
[-1 -1 0 0 -1 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[-2 -1 -1 -1 -1 0 0 -1 0]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{2,6,6,6,6,6,6,6,6,6}
Orbit:
1
{@
Mod: ( 1 -1 0 0 0 -1 0 0 0),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0)
@}
Intersection Matrix:
[-1 2]
[ 2 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[ 5 3 1 2 2 1 1 2 0]
[-2 -1 0 -1 -1 0 -1 -1 0]
[-3 -2 -1 -1 -1 -1 -1 -1 0]
[-1 -1 0 0 -1 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[-2 -1 -1 -1 -1 0 0 -1 0]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
2
{@
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: (0 0 0 0 1 0 0 0 0),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0)
@}
Intersection Matrix:
[-1 0 0 2 1 1]
[ 0 -1 0 1 2 1]
[ 0 0 -1 1 1 2]
[ 2 1 1 -1 0 0]
[ 1 2 1 0 -1 0]
[ 1 1 2 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
3
{@
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: (0 0 0 0 0 0 0 1 0)
@}
Intersection Matrix:
[-1 0 0 1 1 2]
[ 0 -1 1 0 2 1]
[ 0 1 -1 2 0 1]
[ 1 0 2 -1 1 0]
[ 1 2 0 1 -1 0]
[ 2 1 1 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
4
{@
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 1 0 -1 -1 0 0 0 0 0)
@}
Intersection Matrix:
[-1 1 0 1 0 2]
[ 1 -1 2 0 1 0]
[ 0 2 -1 1 0 1]
[ 1 0 1 -1 2 0]
[ 0 1 0 2 -1 1]
[ 2 0 1 0 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
5
{@
Mod: (0 1 0 0 0 0 0 0 0),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 1 0 0 0 0 -1 0 -1 0)
@}
Intersection Matrix:
[-1 1 1 1 1 0]
[ 1 -1 1 1 0 1]
[ 1 1 -1 0 1 1]
[ 1 1 0 -1 1 1]
[ 1 0 1 1 -1 1]
[ 0 1 1 1 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
6
{@
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 1 0 0 0 0 0 -1 -1 0)
@}
Intersection Matrix:
[-1 1 1 0 1 1]
[ 1 -1 1 1 0 1]
[ 1 1 -1 1 1 0]
[ 0 1 1 -1 1 1]
[ 1 0 1 1 -1 1]
[ 1 1 0 1 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
7
{@
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0),
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 1 0 0 -1 0 -1 0 0 0)
@}
Intersection Matrix:
[-1 0 0 0 0 1]
[ 0 -1 0 1 0 0]
[ 0 0 -1 0 1 0]
[ 0 1 0 -1 0 0]
[ 0 0 1 0 -1 0]
[ 1 0 0 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
8
{@
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: (0 0 0 1 0 0 0 0 0)
@}
Intersection Matrix:
[-1 1 0 0 0 0]
[ 1 -1 0 0 0 0]
[ 0 0 -1 0 1 0]
[ 0 0 0 -1 0 1]
[ 0 0 1 0 -1 0]
[ 0 0 0 1 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
9
{@
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 1 -1 -1 0 0 0 0 0 0),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: (0 0 0 0 0 0 1 0 0)
@}
Intersection Matrix:
[-1 0 0 0 0 1]
[ 0 -1 0 1 0 0]
[ 0 0 -1 0 1 0]
[ 0 1 0 -1 0 0]
[ 0 0 1 0 -1 0]
[ 1 0 0 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
10
{@
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0)
@}
Intersection Matrix:
[-1 0 1 0 0 0]
[ 0 -1 0 0 1 0]
[ 1 0 -1 0 0 0]
[ 0 0 0 -1 0 1]
[ 0 1 0 0 -1 0]
[ 0 0 0 1 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
D6(2): C3⋊S3
order := 18,
length := 10080,
subgroup := MatrixGroup(9, Integer Ring) of order 2 * 3^2
Generators:
[ 6 2 3 1 2 2 2 3 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-3 -1 -1 -1 -1 -1 -1 -2 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 0 -1 0 -1 -1 -1 -1 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 0 0 0 1 1 0 1 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 -1 -1 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 1 0 1 1 0 0 0 0]
[-1 0 0 -1 -1 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{2,6,6,6,6,6,6,18}
Orbit:
1
{@
Mod: ( 1 -1 0 0 0 -1 0 0 0),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0)
@}
Intersection Matrix:
[-1 2]
[ 2 -1]
Stabilizer Group Name:
C3^2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 1 1 0 0 0 0]
[-1 0 0 -1 -1 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 0 0 0 1 1 0 1 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 -1 -1 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
2
{@
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: (0 0 0 0 0 0 1 0 0),
Mod: (0 0 0 1 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 1 0 0 0]
[ 0 -1 0 0 1 0]
[ 1 0 -1 0 0 0]
[ 0 0 0 -1 0 1]
[ 0 1 0 0 -1 0]
[ 0 0 0 1 0 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[ 2 0 0 0 1 1 0 1 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 -1 -1 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
3
{@
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: (0 1 0 0 0 0 0 0 0)
@}
Intersection Matrix:
[-1 1 0 1 0 2]
[ 1 -1 2 0 1 0]
[ 0 2 -1 1 0 1]
[ 1 0 1 -1 2 0]
[ 0 1 0 2 -1 1]
[ 2 0 1 0 1 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[ 2 0 0 0 1 1 0 1 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 -1 -1 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
4
{@
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0)
@}
Intersection Matrix:
[-1 1 0 2 0 1]
[ 1 -1 2 0 1 0]
[ 0 2 -1 1 0 1]
[ 2 0 1 -1 1 0]
[ 0 1 0 1 -1 2]
[ 1 0 1 0 2 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 1 1 0 0 0 0]
[-1 0 0 -1 -1 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
5
{@
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 1 0 0 -1 0 -1 0 0 0)
@}
Intersection Matrix:
[-1 0 1 0 0 0]
[ 0 -1 0 0 0 1]
[ 1 0 -1 0 0 0]
[ 0 0 0 -1 1 0]
[ 0 0 0 1 -1 0]
[ 0 1 0 0 0 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[ 2 0 0 0 1 1 0 1 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 -1 -1 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
6
{@
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0)
@}
Intersection Matrix:
[-1 0 0 1 0 0]
[ 0 -1 0 0 0 1]
[ 0 0 -1 0 1 0]
[ 1 0 0 -1 0 0]
[ 0 0 1 0 -1 0]
[ 0 1 0 0 0 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 1 1 0 0 0 0]
[-1 0 0 -1 -1 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
7
{@
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 1 -1 -1 0 0 0 0 0 0),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0)
@}
Intersection Matrix:
[-1 0 1 0 0 0]
[ 0 -1 0 0 1 0]
[ 1 0 -1 0 0 0]
[ 0 0 0 -1 0 1]
[ 0 1 0 0 -1 0]
[ 0 0 0 1 0 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 1 1 0 0 0 0]
[-1 0 0 -1 -1 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
8
{@
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: (0 0 0 0 1 0 0 0 0),
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 1 0 -1 -1 0 0 0 0 0),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 1 0 0 0 0 -1 0 -1 0),
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0)
@}
Intersection Matrix:
[-1 1 0 0 1 0 1 1 1 0 1 0 0 1 0 0 2 1]
[ 1 -1 0 0 0 1 0 0 1 0 1 1 1 0 1 2 0 1]
[ 0 0 -1 0 1 0 0 1 2 1 1 1 1 0 0 1 1 0]
[ 0 0 0 -1 0 0 1 1 1 0 2 0 1 0 1 1 1 1]
[ 1 0 1 0 -1 0 0 1 0 0 1 1 0 1 2 1 0 1]
[ 0 1 0 0 0 -1 0 2 1 1 1 1 0 1 1 0 1 0]
[ 1 0 0 1 0 0 -1 1 1 1 0 2 0 1 1 1 0 0]
[ 1 0 1 1 1 2 1 -1 0 0 0 0 1 0 0 1 0 1]
[ 1 1 2 1 0 1 1 0 -1 0 0 0 0 1 1 0 0 1]
[ 0 0 1 0 0 1 1 0 0 -1 1 0 0 1 1 1 1 2]
[ 1 1 1 2 1 1 0 0 0 1 -1 1 0 1 0 0 0 0]
[ 0 1 1 0 1 1 2 0 0 0 1 -1 1 0 0 0 1 1]
[ 0 1 1 1 0 0 0 1 0 0 0 1 -1 2 1 0 1 1]
[ 1 0 0 0 1 1 1 0 1 1 1 0 2 -1 0 1 0 0]
[ 0 1 0 1 2 1 1 0 1 1 0 0 1 0 -1 0 1 0]
[ 0 2 1 1 1 0 1 1 0 1 0 0 0 1 0 -1 1 0]
[ 2 0 1 1 0 1 0 0 0 1 0 1 1 0 1 1 -1 0]
[ 1 1 0 1 1 0 0 1 1 2 0 1 1 0 0 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
D6(3):D5
order := 10,
length := 36288,
subgroup := MatrixGroup(9, Integer Ring) of order 2 * 5
Generators:
[ 3 1 1 2 1 0 0 1 0]
[-1 -1 0 -1 0 0 0 0 0]
[-1 0 0 -1 0 0 0 -1 0]
[-2 -1 -1 -1 -1 0 0 -1 0]
[-1 0 0 -1 -1 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 0 -1 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 4 2 1 2 1 1 0 2 0]
[-1 0 0 -1 0 0 0 -1 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[-2 -1 -1 -1 -1 0 0 -1 0]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{2,2,2,10,10,10,10,10}
Orbit:
1
{@
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 1 0 -1 0 0 0 0 -1 0)
@}
Intersection Matrix:
[-1 1]
[ 1 -1]
Stabilizer Group Name:
C5
MatrixGroup(9, Integer Ring)
Generators:
[ 4 2 1 2 1 1 0 2 0]
[-1 0 0 -1 0 0 0 -1 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[-2 -1 -1 -1 -1 0 0 -1 0]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
2
{@
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0)
@}
Intersection Matrix:
[-1 1]
[ 1 -1]
Stabilizer Group Name:
C5
MatrixGroup(9, Integer Ring)
Generators:
[ 4 2 1 2 1 1 0 2 0]
[-1 0 0 -1 0 0 0 -1 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[-2 -1 -1 -1 -1 0 0 -1 0]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
3
{@
Mod: ( 1 -1 0 0 0 -1 0 0 0),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0)
@}
Intersection Matrix:
[-1 2]
[ 2 -1]
Stabilizer Group Name:
C5
MatrixGroup(9, Integer Ring)
Generators:
[ 4 2 1 2 1 1 0 2 0]
[-1 0 0 -1 0 0 0 -1 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[-2 -1 -1 -1 -1 0 0 -1 0]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
4
{@
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: ( 1 0 -1 -1 0 0 0 0 0)
@}
Intersection Matrix:
[-1 1 0 1 0 0 1 1 0 2]
[ 1 -1 0 0 0 2 1 1 1 0]
[ 0 0 -1 1 0 1 1 2 0 1]
[ 1 0 1 -1 0 1 1 0 2 0]
[ 0 0 0 0 -1 1 2 1 1 1]
[ 0 2 1 1 1 -1 0 0 0 1]
[ 1 1 1 1 2 0 -1 0 0 0]
[ 1 1 2 0 1 0 0 -1 1 0]
[ 0 1 0 2 1 0 0 1 -1 1]
[ 2 0 1 0 1 1 0 0 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
5
{@
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: (0 1 0 0 0 0 0 0 0)
@}
Intersection Matrix:
[-1 1 1 0 0 1 2 0 0 1]
[ 1 -1 1 0 1 1 0 2 0 0]
[ 1 1 -1 2 1 0 0 0 1 0]
[ 0 0 2 -1 0 1 1 1 0 1]
[ 0 1 1 0 -1 0 1 0 1 2]
[ 1 1 0 1 0 -1 0 0 2 1]
[ 2 0 0 1 1 0 -1 1 1 0]
[ 0 2 0 1 0 0 1 -1 1 1]
[ 0 0 1 0 1 2 1 1 -1 0]
[ 1 0 0 1 2 1 0 1 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
6
{@
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: (0 0 0 0 1 0 0 0 0),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 1 0 0 0 0 -1 0 -1 0)
@}
Intersection Matrix:
[-1 0 1 1 0 1 1 0 0 2]
[ 0 -1 1 1 0 2 1 0 0 1]
[ 1 1 -1 0 2 0 0 1 1 0]
[ 1 1 0 -1 1 0 0 1 2 0]
[ 0 0 2 1 -1 1 1 0 0 1]
[ 1 2 0 0 1 -1 0 1 1 0]
[ 1 1 0 0 1 0 -1 2 1 0]
[ 0 0 1 1 0 1 2 -1 0 1]
[ 0 0 1 2 0 1 1 0 -1 1]
[ 2 1 0 0 1 0 0 1 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
7
{@
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: (0 0 0 1 0 0 0 0 0),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: (0 0 0 0 0 0 1 0 0),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 1 -1 -1 0 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 0 1 0 0 0 0 0 0]
[ 0 -1 0 0 1 0 0 0 0 0]
[ 0 0 -1 0 0 0 0 0 0 1]
[ 1 0 0 -1 0 0 0 0 0 0]
[ 0 1 0 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 -1 0 0 1 0]
[ 0 0 0 0 0 0 -1 1 0 0]
[ 0 0 0 0 0 0 1 -1 0 0]
[ 0 0 0 0 0 1 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
8
{@
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 1 0 0 -1 0 -1 0 0 0),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0)
@}
Intersection Matrix:
[-1 0 1 0 0 0 0 0 0 0]
[ 0 -1 0 0 0 0 0 0 1 0]
[ 1 0 -1 0 0 0 0 0 0 0]
[ 0 0 0 -1 0 0 0 1 0 0]
[ 0 0 0 0 -1 0 1 0 0 0]
[ 0 0 0 0 0 -1 0 0 0 1]
[ 0 0 0 0 1 0 -1 0 0 0]
[ 0 0 0 1 0 0 0 -1 0 0]
[ 0 1 0 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 1 0 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
D6(4):F5
order := 20,
length := 36288,
subgroup := MatrixGroup(9, Integer Ring) of order 2^2 * 5
Generators:
[ 4 2 2 1 2 0 1 1 0]
[-1 -1 0 0 -1 0 0 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 -1 -1 0 0 0 0 0 0]
[-2 -1 -1 -1 -1 0 -1 0 0]
[-2 -1 -1 -1 -1 0 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 6 3 3 2 1 2 2 2 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-3 -2 -1 -1 -1 -1 -1 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-1 -1 -1 0 0 0 0 0 0]
[-2 -1 -1 -1 0 0 -1 -1 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 4 2 1 2 0 1 1 2 0]
[-1 0 0 -1 0 0 0 -1 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 -1 -1 0 0 -1 -1 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[-2 -1 0 -1 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{2,2,2,10,10,10,10,10}
Orbit:
1
{@
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: ( 1 -1 0 0 0 0 -1 0 0)
@}
Intersection Matrix:
[-1 1]
[ 1 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[ 4 2 1 2 0 1 1 2 0]
[-1 0 0 -1 0 0 0 -1 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 -1 -1 0 0 -1 -1 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[-2 -1 0 -1 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 6 3 3 2 1 2 2 2 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-3 -2 -1 -1 -1 -1 -1 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-1 -1 -1 0 0 0 0 0 0]
[-2 -1 -1 -1 0 0 -1 -1 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
2
{@
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0)
@}
Intersection Matrix:
[-1 1]
[ 1 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[ 4 2 1 2 0 1 1 2 0]
[-1 0 0 -1 0 0 0 -1 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 -1 -1 0 0 -1 -1 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[-2 -1 0 -1 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 6 3 3 2 1 2 2 2 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-3 -2 -1 -1 -1 -1 -1 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-1 -1 -1 0 0 0 0 0 0]
[-2 -1 -1 -1 0 0 -1 -1 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
3
{@
Mod: ( 1 -1 0 0 0 -1 0 0 0),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0)
@}
Intersection Matrix:
[-1 2]
[ 2 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[ 4 2 1 2 0 1 1 2 0]
[-1 0 0 -1 0 0 0 -1 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 -1 -1 0 0 -1 -1 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[-2 -1 0 -1 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 6 3 3 2 1 2 2 2 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-3 -2 -1 -1 -1 -1 -1 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-1 -1 -1 0 0 0 0 0 0]
[-2 -1 -1 -1 0 0 -1 -1 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
4
{@
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: (0 0 0 0 0 0 1 0 0),
Mod: ( 1 0 0 0 0 -1 0 -1 0)
@}
Intersection Matrix:
[-1 0 0 1 2 0 1 0 1 1]
[ 0 -1 0 2 1 0 1 0 1 1]
[ 0 0 -1 1 1 0 1 0 1 2]
[ 1 2 1 -1 0 1 0 1 0 0]
[ 2 1 1 0 -1 1 0 1 0 0]
[ 0 0 0 1 1 -1 1 0 2 1]
[ 1 1 1 0 0 1 -1 2 0 0]
[ 0 0 0 1 1 0 2 -1 1 1]
[ 1 1 1 0 0 2 0 1 -1 0]
[ 1 1 2 0 0 1 0 1 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 0 1 0 1 1 2 0]
[-1 0 0 -1 0 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[-1 0 0 0 0 -1 0 -1 0]
[-2 -1 0 -1 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
5
{@
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 1 0 -1 -1 0 0 0 0 0),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 1 0 -1 0 -1 0 0 0 0)
@}
Intersection Matrix:
[-1 0 0 1 1 1 1 1 1 0]
[ 0 -1 1 0 1 1 1 1 0 1]
[ 0 1 -1 1 1 0 1 0 1 1]
[ 1 0 1 -1 1 0 0 1 1 1]
[ 1 1 1 1 -1 0 1 1 0 0]
[ 1 1 0 0 0 -1 1 1 1 1]
[ 1 1 1 0 1 1 -1 0 1 0]
[ 1 1 0 1 1 1 0 -1 0 1]
[ 1 0 1 1 0 1 1 0 -1 1]
[ 0 1 1 1 0 1 0 1 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 2 1 1 1 0 0 1 0]
[-2 -1 -1 -1 -1 0 0 -1 0]
[-1 -1 0 -1 0 0 0 0 0]
[-1 -1 -1 0 0 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 1 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
6
{@
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: (0 1 0 0 0 0 0 0 0),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0)
@}
Intersection Matrix:
[-1 0 1 1 0 1 1 0 1 1]
[ 0 -1 1 1 1 1 1 1 0 0]
[ 1 1 -1 0 0 1 1 1 0 1]
[ 1 1 0 -1 1 1 1 0 1 0]
[ 0 1 0 1 -1 1 0 1 1 1]
[ 1 1 1 1 1 -1 0 0 0 1]
[ 1 1 1 1 0 0 -1 1 1 0]
[ 0 1 1 0 1 0 1 -1 1 1]
[ 1 0 0 1 1 0 1 1 -1 1]
[ 1 0 1 0 1 1 0 1 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 5 2 2 0 2 2 2 2 0]
[-2 0 -1 0 -1 -1 -1 -1 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
7
{@
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 1 -1 -1 0 0 0 0 0 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: (0 0 0 0 1 0 0 0 0),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: (0 0 0 1 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 0 0 0 1 0 0 0 0]
[ 0 -1 0 0 0 0 0 0 1 0]
[ 0 0 -1 0 0 0 0 0 0 1]
[ 0 0 0 -1 0 0 0 1 0 0]
[ 0 0 0 0 -1 0 1 0 0 0]
[ 1 0 0 0 0 -1 0 0 0 0]
[ 0 0 0 0 1 0 -1 0 0 0]
[ 0 0 0 1 0 0 0 -1 0 0]
[ 0 1 0 0 0 0 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 0 1 0 1 1 2 0]
[-1 0 0 -1 0 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[-1 0 0 0 0 -1 0 -1 0]
[-2 -1 0 -1 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
8
{@
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: ( 1 0 0 -1 0 -1 0 0 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0)
@}
Intersection Matrix:
[-1 0 0 0 0 0 0 1 0 0]
[ 0 -1 0 0 0 0 1 0 0 0]
[ 0 0 -1 0 0 1 0 0 0 0]
[ 0 0 0 -1 0 0 0 0 0 1]
[ 0 0 0 0 -1 0 0 0 1 0]
[ 0 0 1 0 0 -1 0 0 0 0]
[ 0 1 0 0 0 0 -1 0 0 0]
[ 1 0 0 0 0 0 0 -1 0 0]
[ 0 0 0 0 1 0 0 0 -1 0]
[ 0 0 0 1 0 0 0 0 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 5 2 2 0 2 2 2 2 0]
[-2 0 -1 0 -1 -1 -1 -1 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
D6(5):D6
order := 12,
length := 60480,
subgroup := MatrixGroup(9, Integer Ring) of order 2^2 * 3
Generators:
[ 4 1 1 1 1 1 1 3 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 -1 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[-3 -1 -1 -1 -1 -1 -1 -2 0]
[ 0 0 0 0 0 0 0 0 1]
[ 5 2 1 1 2 2 1 3 0]
[-3 -1 -1 -1 -1 -1 -1 -2 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 0 1 0 1 1 0 0 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 -1 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 0 0 0 -1 -1 0 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{2,6,12,12,12,12}
Orbit:
1
{@
Mod: ( 1 -1 0 0 0 -1 0 0 0),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0)
@}
Intersection Matrix:
[-1 2]
[ 2 -1]
Stabilizer Group Name:
C6
MatrixGroup(9, Integer Ring)
Generators:
[ 2 0 1 0 1 1 0 0 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 -1 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 0 0 0 -1 -1 0 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 5 2 1 1 2 2 1 3 0]
[-3 -1 -1 -1 -1 -1 -1 -2 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
2
{@
Mod: (0 1 0 0 0 0 0 0 0),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 1 0 0 0 0 -1 0 -1 0),
Mod: (0 0 0 0 0 0 0 1 0)
@}
Intersection Matrix:
[-1 2 1 1 0 0]
[ 2 -1 0 0 1 1]
[ 1 0 -1 1 0 2]
[ 1 0 1 -1 2 0]
[ 0 1 0 2 -1 1]
[ 0 1 2 0 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 0 1 0 1 1 0 0 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 -1 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 0 0 0 -1 -1 0 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
3
{@
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: ( 1 0 -1 -1 0 0 0 0 0),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: (0 0 0 0 1 0 0 0 0)
@}
Intersection Matrix:
[-1 0 0 0 1 1 0 2 0 1 1 1]
[ 0 -1 0 1 1 2 0 1 1 0 0 1]
[ 0 0 -1 1 2 1 0 1 1 0 0 1]
[ 0 1 1 -1 0 0 0 1 0 2 1 1]
[ 1 1 2 0 -1 0 1 0 0 1 1 0]
[ 1 2 1 0 0 -1 1 0 0 1 1 0]
[ 0 0 0 0 1 1 -1 1 0 1 1 2]
[ 2 1 1 1 0 0 1 -1 1 0 0 0]
[ 0 1 1 0 0 0 0 1 -1 1 2 1]
[ 1 0 0 2 1 1 1 0 1 -1 0 0]
[ 1 0 0 1 1 1 1 0 2 0 -1 0]
[ 1 1 1 1 0 0 2 0 1 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
4
{@
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0)
@}
Intersection Matrix:
[-1 0 1 0 1 2 1 0 1 0 0 1]
[ 0 -1 1 0 1 1 2 0 1 0 0 1]
[ 1 1 -1 2 0 0 0 1 0 1 1 0]
[ 0 0 2 -1 1 1 1 0 1 0 0 1]
[ 1 1 0 1 -1 0 0 2 0 1 1 0]
[ 2 1 0 1 0 -1 0 1 0 1 1 0]
[ 1 2 0 1 0 0 -1 1 0 1 1 0]
[ 0 0 1 0 2 1 1 -1 1 0 0 1]
[ 1 1 0 1 0 0 0 1 -1 1 2 0]
[ 0 0 1 0 1 1 1 0 1 -1 0 2]
[ 0 0 1 0 1 1 1 0 2 0 -1 1]
[ 1 1 0 1 0 0 0 1 0 2 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
5
{@
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: (0 0 0 1 0 0 0 0 0),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: (0 0 0 0 0 0 1 0 0),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 1 -1 -1 0 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 0 0 1 0 0 0 0 0 0 0]
[ 0 -1 0 0 0 1 0 0 0 0 0 0]
[ 0 0 -1 0 0 0 0 0 0 0 0 1]
[ 0 0 0 -1 0 0 1 0 0 0 0 0]
[ 1 0 0 0 -1 0 0 0 0 0 0 0]
[ 0 1 0 0 0 -1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 -1 0 0 1 0]
[ 0 0 0 0 0 0 0 0 -1 1 0 0]
[ 0 0 0 0 0 0 0 0 1 -1 0 0]
[ 0 0 0 0 0 0 0 1 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
6
{@
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 1 0 0 -1 0 -1 0 0 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0)
@}
Intersection Matrix:
[-1 0 0 1 0 0 0 0 0 0 0 0]
[ 0 -1 0 0 0 0 0 0 0 0 1 0]
[ 0 0 -1 0 0 1 0 0 0 0 0 0]
[ 1 0 0 -1 0 0 0 0 0 0 0 0]
[ 0 0 0 0 -1 0 0 0 0 1 0 0]
[ 0 0 1 0 0 -1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 -1 1 0 0 0 0]
[ 0 0 0 0 0 0 1 -1 0 0 0 0]
[ 0 0 0 0 0 0 0 0 -1 0 0 1]
[ 0 0 0 0 1 0 0 0 0 -1 0 0]
[ 0 1 0 0 0 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 0 0 1 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
D6(6):D6
order := 12,
length := 60480,
subgroup := MatrixGroup(9, Integer Ring) of order 2^2 * 3
Generators:
[ 4 2 2 1 2 1 1 0 0]
[-2 -1 -1 -1 -1 0 -1 0 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[-2 -1 -1 -1 -1 -1 0 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[-1 -1 -1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 5 2 1 1 2 2 1 3 0]
[-3 -1 -1 -1 -1 -1 -1 -2 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 6 3 2 2 2 1 2 3 0]
[-3 -2 -1 -1 -1 -1 -1 -1 0]
[-2 -1 0 -1 -1 0 -1 -1 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[-2 -1 -1 -1 0 0 -1 -1 0]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 -1 -1 -1 0 0 -1 0]
[-3 -1 -1 -1 -1 -1 -1 -2 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{2,6,6,6,12,12,12,}
Orbit:
1
{@
Mod: ( 1 -1 0 0 0 -1 0 0 0),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0)
@}
Intersection Matrix:
[-1 2]
[ 2 -1]
Stabilizer Group Name:
S3
MatrixGroup(9, Integer Ring)
Generators:
[ 5 2 1 1 2 2 1 3 0]
[-3 -1 -1 -1 -1 -1 -1 -2 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 4 2 2 1 2 1 1 0 0]
[-2 -1 -1 -1 -1 0 -1 0 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[-2 -1 -1 -1 -1 -1 0 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[-1 -1 -1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
2
{@
Mod: (0 1 0 0 0 0 0 0 0),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 1 0 0 0 0 -1 0 -1 0),
Mod: (0 0 0 0 0 0 0 1 0)
@}
Intersection Matrix:
[-1 2 1 1 0 0]
[ 2 -1 0 0 1 1]
[ 1 0 -1 1 0 2]
[ 1 0 1 -1 2 0]
[ 0 1 0 2 -1 1]
[ 0 1 2 0 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 0 1 0 0 1 0 1 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 -1 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 -1 0 0 0 0 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
3
{@
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: ( 1 0 -1 -1 0 0 0 0 0)
@}
Intersection Matrix:
[-1 1 1 1 1 0]
[ 1 -1 1 1 0 1]
[ 1 1 -1 0 1 1]
[ 1 1 0 -1 1 1]
[ 1 0 1 1 -1 1]
[ 0 1 1 1 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 4 2 2 1 2 1 1 0 0]
[-2 -1 -1 -1 -1 0 -1 0 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[-2 -1 -1 -1 -1 -1 0 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[-1 -1 -1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
4
{@
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: (0 0 0 0 1 0 0 0 0),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: ( 1 0 0 0 -1 0 -1 0 0)
@}
Intersection Matrix:
[-1 1 1 1 1 0]
[ 1 -1 1 1 0 1]
[ 1 1 -1 0 1 1]
[ 1 1 0 -1 1 1]
[ 1 0 1 1 -1 1]
[ 0 1 1 1 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 4 2 2 1 2 1 1 0 0]
[-2 -1 -1 -1 -1 0 -1 0 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[-2 -1 -1 -1 -1 -1 0 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[-1 -1 -1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
5
{@
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0)
@}
Intersection Matrix:
[-1 0 1 0 1 2 1 0 1 0 0 1]
[ 0 -1 1 0 1 1 2 0 1 0 0 1]
[ 1 1 -1 2 0 0 0 1 0 1 1 0]
[ 0 0 2 -1 1 1 1 0 1 0 0 1]
[ 1 1 0 1 -1 0 0 2 0 1 1 0]
[ 2 1 0 1 0 -1 0 1 0 1 1 0]
[ 1 2 0 1 0 0 -1 1 0 1 1 0]
[ 0 0 1 0 2 1 1 -1 1 0 0 1]
[ 1 1 0 1 0 0 0 1 -1 1 2 0]
[ 0 0 1 0 1 1 1 0 1 -1 0 2]
[ 0 0 1 0 1 1 1 0 2 0 -1 1]
[ 1 1 0 1 0 0 0 1 0 2 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
6
{@
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 1 0 0 -1 0 -1 0 0 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0)
@}
Intersection Matrix:
[-1 0 0 0 0 0 0 0 0 0 1 0]
[ 0 -1 0 1 0 0 0 0 0 0 0 0]
[ 0 0 -1 0 0 1 0 0 0 0 0 0]
[ 0 1 0 -1 0 0 0 0 0 0 0 0]
[ 0 0 0 0 -1 0 0 0 0 1 0 0]
[ 0 0 1 0 0 -1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 -1 1 0 0 0 0]
[ 0 0 0 0 0 0 1 -1 0 0 0 0]
[ 0 0 0 0 0 0 0 0 -1 0 0 1]
[ 0 0 0 0 1 0 0 0 0 -1 0 0]
[ 1 0 0 0 0 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 0 0 1 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
7
{@
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: (0 0 0 1 0 0 0 0 0),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: (0 0 0 0 0 0 1 0 0),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 1 -1 -1 0 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 0 0 1 0 0 0 0 0 0 0]
[ 0 -1 0 0 0 1 0 0 0 0 0 0]
[ 0 0 -1 0 0 0 0 0 0 0 0 1]
[ 0 0 0 -1 0 0 1 0 0 0 0 0]
[ 1 0 0 0 -1 0 0 0 0 0 0 0]
[ 0 1 0 0 0 -1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 -1 0 0 1 0]
[ 0 0 0 0 0 0 0 0 -1 1 0 0]
[ 0 0 0 0 0 0 0 0 1 -1 0 0]
[ 0 0 0 0 0 0 0 1 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
D6(7):S4
order := 24,
length := 15120,
subgroup := MatrixGroup(9, Integer Ring) of order 2^3 * 3
Generators:
[ 6 2 2 1 3 2 2 3 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-2 0 -1 0 -1 -1 -1 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[-3 -1 -1 -1 -1 -1 -1 -2 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 3 1 1 0 2 1 1 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[ 0 0 0 0 0 0 0 1 0]
[-1 -1 0 0 -1 0 0 0 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 0 0 0 -1 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 5 2 2 0 2 2 2 2 0]
[-2 0 -1 0 -1 -1 -1 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 1 0 1 0 0 0 1 0]
[-1 0 0 -1 0 0 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{2,6,12,12,24}
Orbit:
1
{@
Mod: ( 1 -1 0 0 0 -1 0 0 0),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0)
@}
Intersection Matrix:
[-1 2]
[ 2 -1]
Stabilizer Group Name:
A4
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 1 0 0 0 1 0]
[-1 0 0 -1 0 0 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 3 1 1 0 2 1 1 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[ 0 0 0 0 0 0 0 1 0]
[-1 -1 0 0 -1 0 0 0 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 0 0 0 -1 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 5 2 2 0 2 2 2 2 0]
[-2 0 -1 0 -1 -1 -1 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
2
{@
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 1 0 0 0 0 -1 0 -1 0),
Mod: ( 1 0 0 0 0 0 -1 -1 0)
@}
Intersection Matrix:
[-1 0 1 2 0 1]
[ 0 -1 0 1 1 2]
[ 1 0 -1 0 2 1]
[ 2 1 0 -1 1 0]
[ 0 1 2 1 -1 0]
[ 1 2 1 0 0 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 1 0 0 0 1 0]
[-1 0 0 -1 0 0 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 5 2 2 0 2 2 2 2 0]
[-2 0 -1 0 -1 -1 -1 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
3
{@
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 1 0 0 -1 0 -1 0 0 0),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0)
@}
Intersection Matrix:
[-1 0 0 0 0 0 0 0 0 0 1 0]
[ 0 -1 0 1 0 0 0 0 0 0 0 0]
[ 0 0 -1 0 0 1 0 0 0 0 0 0]
[ 0 1 0 -1 0 0 0 0 0 0 0 0]
[ 0 0 0 0 -1 0 0 0 0 1 0 0]
[ 0 0 1 0 0 -1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 -1 0 1 0 0 0]
[ 0 0 0 0 0 0 0 -1 0 0 0 1]
[ 0 0 0 0 0 0 1 0 -1 0 0 0]
[ 0 0 0 0 1 0 0 0 0 -1 0 0]
[ 1 0 0 0 0 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 0 1 0 0 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 6 3 2 1 2 2 2 3 0]
[-3 -1 -1 -1 -1 -1 -1 -2 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-3 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
4
{@
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: (0 0 0 1 0 0 0 0 0),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: (0 0 0 0 0 0 1 0 0),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 1 -1 -1 0 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 0 0 1 0 0 0 0 0 0 0]
[ 0 -1 0 0 0 1 0 0 0 0 0 0]
[ 0 0 -1 0 0 0 0 0 0 0 0 1]
[ 0 0 0 -1 0 0 1 0 0 0 0 0]
[ 1 0 0 0 -1 0 0 0 0 0 0 0]
[ 0 1 0 0 0 -1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 -1 0 0 1 0]
[ 0 0 0 0 0 0 0 0 -1 1 0 0]
[ 0 0 0 0 0 0 0 0 1 -1 0 0]
[ 0 0 0 0 0 0 0 1 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0 0 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 6 3 2 1 2 2 2 3 0]
[-3 -1 -1 -1 -1 -1 -1 -2 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-3 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
5
{@
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: (0 0 0 0 1 0 0 0 0),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 1 0 -1 -1 0 0 0 0 0),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: (0 1 0 0 0 0 0 0 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0)
@}
Intersection Matrix:
[-1 0 0 0 0 1 1 1 0 0 1 0 1 0 1 1 1 0 0 0 1 1 2 1]
[ 0 -1 0 1 1 1 0 2 0 1 1 1 1 0 1 0 1 0 0 0 1 0 1 0]
[ 0 0 -1 0 0 0 1 1 0 0 2 1 1 0 1 0 1 0 0 1 1 1 1 1]
[ 0 1 0 -1 0 1 2 0 1 0 1 1 0 0 0 0 1 0 1 0 1 1 1 1]
[ 0 1 0 0 -1 0 1 0 0 0 1 0 1 0 0 1 0 1 1 1 1 2 1 1]
[ 1 1 0 1 0 -1 0 0 0 0 1 0 1 1 1 1 0 1 0 2 0 1 0 1]
[ 1 0 1 2 1 0 -1 1 0 1 0 0 1 1 1 1 0 1 0 1 0 0 0 0]
[ 1 2 1 0 0 0 1 -1 1 0 0 0 0 1 0 1 0 1 1 1 0 1 0 1]
[ 0 0 0 1 0 0 0 1 -1 1 1 0 2 1 1 1 1 0 0 1 0 1 1 0]
[ 0 1 0 0 0 0 1 0 1 -1 1 0 0 0 1 1 0 1 0 1 1 1 1 2]
[ 1 1 2 1 1 1 0 0 1 1 -1 0 0 1 0 1 0 1 1 0 0 0 0 0]
[ 0 1 1 1 0 0 0 0 0 0 0 -1 1 1 1 2 0 1 0 1 0 1 1 1]
[ 1 1 1 0 1 1 1 0 2 0 0 1 -1 0 0 0 0 1 1 0 1 0 0 1]
[ 0 0 0 0 0 1 1 1 1 0 1 1 0 -1 0 0 0 1 1 0 2 1 1 1]
[ 1 1 1 0 0 1 1 0 1 1 0 1 0 0 -1 0 0 1 2 0 1 1 0 0]
[ 1 0 0 0 1 1 1 1 1 1 1 2 0 0 0 -1 1 0 1 0 1 0 0 0]
[ 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 -1 2 1 1 1 1 0 1]
[ 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 0 2 -1 0 0 0 0 1 0]
[ 0 0 0 1 1 0 0 1 0 0 1 0 1 1 2 1 1 0 -1 1 0 0 1 1]
[ 0 0 1 0 1 2 1 1 1 1 0 1 0 0 0 0 1 0 1 -1 1 0 1 0]
[ 1 1 1 1 1 0 0 0 0 1 0 0 1 2 1 1 1 0 0 1 -1 0 0 0]
[ 1 0 1 1 2 1 0 1 1 1 0 1 0 1 1 0 1 0 0 0 0 -1 0 0]
[ 2 1 1 1 1 0 0 0 1 1 0 1 0 1 0 0 0 1 1 1 0 0 -1 0]
[ 1 0 1 1 1 1 0 1 0 2 0 1 1 1 0 0 1 0 1 0 0 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
D6(8):S4
order := 24,
length := 15120,
subgroup := MatrixGroup(9, Integer Ring) of order 2^3 * 3
Generators:
[ 4 1 1 2 2 1 0 2 0]
[-1 0 0 -1 0 0 0 -1 0]
[-1 0 0 -1 -1 0 0 0 0]
[-2 -1 -1 -1 -1 0 0 -1 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 3 1 0 0 1 1 2 1 0]
[-1 0 0 0 0 0 -1 -1 0]
[-1 0 0 0 -1 0 -1 0 0]
[-1 -1 0 0 0 0 -1 0 0]
[-1 0 0 0 0 -1 -1 0 0]
[ 0 0 1 0 0 0 0 0 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 3 0 1 1 0 1 2 1 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 -1 0 0 -1 0 0]
[-1 0 -1 0 0 0 -1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[-2 0 -1 -1 0 -1 -1 -1 0]
[-1 0 0 0 0 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 3 1 0 0 1 1 2 1 0]
[-1 0 0 0 -1 0 -1 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 -1 0 0 0 0 -1 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-1 0 0 0 0 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{4,4,6,6,12,12,12}
Orbit:
1
{@
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 1 0 0 0 0 -1 0 -1 0),
Mod: ( 1 0 -1 -1 0 0 0 0 0)
@}
Intersection Matrix:
[-1 1 1 1]
[ 1 -1 1 1]
[ 1 1 -1 1]
[ 1 1 1 -1]
Stabilizer Group Name:
S3
MatrixGroup(9, Integer Ring)
Generators:
[ 4 1 1 2 2 1 0 2 0]
[-1 0 0 -1 0 0 0 -1 0]
[-1 0 0 -1 -1 0 0 0 0]
[-2 -1 -1 -1 -1 0 0 -1 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 3 1 0 0 1 1 2 1 0]
[-1 0 0 0 0 0 -1 -1 0]
[-1 0 0 0 -1 0 -1 0 0]
[-1 -1 0 0 0 0 -1 0 0]
[-1 0 0 0 0 -1 -1 0 0]
[ 0 0 1 0 0 0 0 0 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
2
{@
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: (0 0 0 0 0 0 1 0 0)
@}
Intersection Matrix:
[-1 1 1 1]
[ 1 -1 1 1]
[ 1 1 -1 1]
[ 1 1 1 -1]
Stabilizer Group Name:
S3
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 1 1 0 2 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[-1 -1 0 0 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 1 0]
[-1 0 0 -1 0 0 -1 0 0]
[-2 -1 -1 -1 -1 0 -1 0 0]
[-1 0 -1 0 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 4 1 1 2 2 1 0 2 0]
[-1 0 0 -1 -1 0 0 0 0]
[-1 0 0 0 -1 0 0 -1 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[-2 -1 -1 -1 -1 0 0 -1 0]
[-1 0 0 -1 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
3
{@
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0),
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0)
@}
Intersection Matrix:
[-1 1 0 1 1 1]
[ 1 -1 1 1 0 1]
[ 0 1 -1 1 1 1]
[ 1 1 1 -1 1 0]
[ 1 0 1 1 -1 1]
[ 1 1 1 0 1 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 4 1 1 2 2 1 0 2 0]
[-1 0 0 -1 0 0 0 -1 0]
[-1 0 0 -1 -1 0 0 0 0]
[-2 -1 -1 -1 -1 0 0 -1 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 3 0 1 1 0 1 2 1 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 -1 0 0 -1 0 0]
[-1 0 -1 0 0 0 -1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[-2 0 -1 -1 0 -1 -1 -1 0]
[-1 0 0 0 0 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
4
{@
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: ( 1 0 0 -1 0 -1 0 0 0)
@}
Intersection Matrix:
[-1 1 1 1 0 1]
[ 1 -1 0 1 1 1]
[ 1 0 -1 1 1 1]
[ 1 1 1 -1 1 0]
[ 0 1 1 1 -1 1]
[ 1 1 1 0 1 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 6 2 2 3 3 1 2 2 0]
[-2 0 -1 -1 -1 0 -1 -1 0]
[-2 -1 0 -1 -1 0 -1 -1 0]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
[-3 -1 -1 -2 -1 -1 -1 -1 0]
[-1 0 0 -1 -1 0 0 0 0]
[-2 -1 -1 -1 -1 0 -1 0 0]
[-2 -1 -1 -1 -1 0 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 3 1 1 1 1 0 2 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[-1 0 0 -1 0 0 -1 0 0]
[-1 0 -1 0 0 0 -1 0 0]
[-1 -1 0 0 0 0 -1 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-2 -1 -1 -1 -1 0 -1 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
5
{@
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: (0 0 0 0 1 0 0 0 0),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: (0 0 0 1 0 0 0 0 0)
@}
Intersection Matrix:
[-1 1 1 0 1 1 0 1 0 0 0 2]
[ 1 -1 0 2 0 0 1 0 1 1 1 0]
[ 1 0 -1 1 0 0 1 0 1 1 2 0]
[ 0 2 1 -1 1 1 0 1 0 0 0 1]
[ 1 0 0 1 -1 0 1 0 1 2 1 0]
[ 1 0 0 1 0 -1 2 0 1 1 1 0]
[ 0 1 1 0 1 2 -1 1 0 0 0 1]
[ 1 0 0 1 0 0 1 -1 2 1 1 0]
[ 0 1 1 0 1 1 0 2 -1 0 0 1]
[ 0 1 1 0 2 1 0 1 0 -1 0 1]
[ 0 1 2 0 1 1 0 1 0 0 -1 1]
[ 2 0 0 1 0 0 1 0 1 1 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 0 0 1 1 2 1 0]
[-1 0 0 0 -1 0 -1 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 -1 0 0 0 0 -1 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-1 0 0 0 0 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
6
{@
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: (0 1 0 0 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 0 0 1 0 0 0 0 0 0 0]
[ 0 -1 1 0 0 0 0 0 0 0 0 0]
[ 0 1 -1 0 0 0 0 0 0 0 0 0]
[ 0 0 0 -1 0 0 0 0 0 1 0 0]
[ 1 0 0 0 -1 0 0 0 0 0 0 0]
[ 0 0 0 0 0 -1 0 1 0 0 0 0]
[ 0 0 0 0 0 0 -1 0 0 0 1 0]
[ 0 0 0 0 0 1 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 0 0 -1 0 0 1]
[ 0 0 0 1 0 0 0 0 0 -1 0 0]
[ 0 0 0 0 0 0 1 0 0 0 -1 0]
[ 0 0 0 0 0 0 0 0 1 0 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 0 0 1 1 2 1 0]
[-1 0 0 0 -1 0 -1 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 -1 0 0 0 0 -1 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-1 0 0 0 0 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
7
{@
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: ( 1 -1 -1 0 0 0 0 0 0),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 1 -1 0 0 0 -1 0 0 0)
@}
Intersection Matrix:
[-1 0 0 0 0 0 0 0 0 0 1 0]
[ 0 -1 0 0 0 0 0 0 0 1 0 0]
[ 0 0 -1 0 1 0 0 0 0 0 0 0]
[ 0 0 0 -1 0 0 0 1 0 0 0 0]
[ 0 0 1 0 -1 0 0 0 0 0 0 0]
[ 0 0 0 0 0 -1 0 0 1 0 0 0]
[ 0 0 0 0 0 0 -1 0 0 0 0 1]
[ 0 0 0 1 0 0 0 -1 0 0 0 0]
[ 0 0 0 0 0 1 0 0 -1 0 0 0]
[ 0 1 0 0 0 0 0 0 0 -1 0 0]
[ 1 0 0 0 0 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0 0 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 0 1 1 0 1 2 1 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 -1 0 0 -1 0 0]
[-1 0 -1 0 0 0 -1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[-2 0 -1 -1 0 -1 -1 -1 0]
[-1 0 0 0 0 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
D6(9):S4
order := 24,
length := 15120,
subgroup := MatrixGroup(9, Integer Ring) of order 2^3 * 3
Generators:
[ 6 2 1 2 3 2 3 2 0]
[-2 0 0 -1 -1 -1 -1 -1 0]
[-1 0 0 0 -1 0 -1 0 0]
[-2 -1 0 -1 -1 -1 -1 0 0]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
[-2 -1 0 -1 -1 0 -1 -1 0]
[-3 -1 -1 -1 -1 -1 -2 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 3 0 1 1 0 1 1 2 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 1 0 0 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 -1 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 0 -1 -1 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 1 0 1 0 0 0 1 0]
[-1 0 0 -1 0 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 0 0 0 1 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 1 0 1 0 0 0 1 0]
[-1 0 0 -1 0 0 0 -1 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{6,6,8,12,12,12}
Orbit:
1
{@
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: (0 0 0 0 0 0 0 1 0)
@}
Intersection Matrix:
[-1 1 0 1 1 1]
[ 1 -1 1 0 1 1]
[ 0 1 -1 1 1 1]
[ 1 0 1 -1 1 1]
[ 1 1 1 1 -1 0]
[ 1 1 1 1 0 -1]
Stabilizer Group Name:
C4
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 1 0 0 0 1 0]
[-1 0 0 -1 0 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 0 0 0 1 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 6 1 2 3 2 2 3 2 0]
[-1 0 0 -1 0 0 -1 0 0]
[-2 0 0 -1 -1 -1 -1 -1 0]
[-3 -1 -1 -1 -1 -1 -2 -1 0]
[-3 -1 -1 -2 -1 -1 -1 -1 0]
[-2 0 -1 -1 -1 0 -1 -1 0]
[-2 0 -1 -1 -1 -1 -1 0 0]
[-2 0 -1 -1 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
2
{@
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: ( 1 0 -1 -1 0 0 0 0 0),
Mod: ( 1 0 0 -1 0 -1 0 0 0)
@}
Intersection Matrix:
[-1 1 0 1 1 1]
[ 1 -1 1 0 1 1]
[ 0 1 -1 1 1 1]
[ 1 0 1 -1 1 1]
[ 1 1 1 1 -1 0]
[ 1 1 1 1 0 -1]
Stabilizer Group Name:
C4
MatrixGroup(9, Integer Ring)
Generators:
[ 6 2 2 2 3 1 3 2 0]
[-2 0 -1 -1 -1 0 -1 -1 0]
[-1 0 0 0 -1 0 -1 0 0]
[-2 -1 -1 -1 -1 0 -1 0 0]
[-3 -1 -1 -1 -1 -1 -2 -1 0]
[-2 -1 0 -1 -1 0 -1 -1 0]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 1 0 1 0 0 0 1 0]
[-1 0 0 -1 0 0 0 -1 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
3
{@
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0)
@}
Intersection Matrix:
[-1 1 1 1 0 0 0 2]
[ 1 -1 1 1 0 0 2 0]
[ 1 1 -1 1 2 0 0 0]
[ 1 1 1 -1 0 2 0 0]
[ 0 0 2 0 -1 1 1 1]
[ 0 0 0 2 1 -1 1 1]
[ 0 2 0 0 1 1 -1 1]
[ 2 0 0 0 1 1 1 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 1 0 1 2 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
4
{@
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: (0 0 0 1 0 0 0 0 0),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: (0 0 0 0 0 0 1 0 0),
Mod: ( 1 0 0 0 0 -1 0 -1 0),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0),
Mod: (0 0 0 0 1 0 0 0 0)
@}
Intersection Matrix:
[-1 2 0 0 0 1 1 0 1 1 0 1]
[ 2 -1 1 1 1 0 0 1 0 0 1 0]
[ 0 1 -1 0 0 1 1 0 1 2 0 1]
[ 0 1 0 -1 0 1 1 0 1 1 0 2]
[ 0 1 0 0 -1 1 1 0 2 1 0 1]
[ 1 0 1 1 1 -1 0 2 0 0 1 0]
[ 1 0 1 1 1 0 -1 1 0 0 2 0]
[ 0 1 0 0 0 2 1 -1 1 1 0 1]
[ 1 0 1 1 2 0 0 1 -1 0 1 0]
[ 1 0 2 1 1 0 0 1 0 -1 1 0]
[ 0 1 0 0 0 1 2 0 1 1 -1 1]
[ 1 0 1 2 1 0 0 1 0 0 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 1 0 0 0 1 0]
[-1 0 0 -1 0 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 0 0 0 1 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
5
{@
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: (0 1 0 0 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 0 0 1 0 0 0 0 0 0 0]
[ 0 -1 1 0 0 0 0 0 0 0 0 0]
[ 0 1 -1 0 0 0 0 0 0 0 0 0]
[ 0 0 0 -1 0 0 0 0 1 0 0 0]
[ 1 0 0 0 -1 0 0 0 0 0 0 0]
[ 0 0 0 0 0 -1 0 1 0 0 0 0]
[ 0 0 0 0 0 0 -1 0 0 0 1 0]
[ 0 0 0 0 0 1 0 -1 0 0 0 0]
[ 0 0 0 1 0 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 0 -1 0 1]
[ 0 0 0 0 0 0 1 0 0 0 -1 0]
[ 0 0 0 0 0 0 0 0 0 1 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 1 0 0 0 1 0]
[-1 0 0 -1 0 0 0 -1 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
6
{@
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: ( 1 -1 -1 0 0 0 0 0 0),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 1 -1 0 0 0 -1 0 0 0)
@}
Intersection Matrix:
[-1 0 0 0 0 0 0 0 0 0 1 0]
[ 0 -1 0 0 0 0 0 0 0 1 0 0]
[ 0 0 -1 0 1 0 0 0 0 0 0 0]
[ 0 0 0 -1 0 0 0 1 0 0 0 0]
[ 0 0 1 0 -1 0 0 0 0 0 0 0]
[ 0 0 0 0 0 -1 0 0 1 0 0 0]
[ 0 0 0 0 0 0 -1 0 0 0 0 1]
[ 0 0 0 1 0 0 0 -1 0 0 0 0]
[ 0 0 0 0 0 1 0 0 -1 0 0 0]
[ 0 1 0 0 0 0 0 0 0 -1 0 0]
[ 1 0 0 0 0 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0 0 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
D6(10):S3^2
order := 36,
length := 20160,
subgroup := MatrixGroup(9, Integer Ring) of order 2^2 * 3^2
Generators:
[ 4 2 0 1 2 1 1 2 0]
[-2 -1 0 -1 -1 0 -1 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 5 2 2 2 1 1 1 3 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[-2 -1 -1 -1 0 0 -1 -1 0]
[-2 -1 -1 -1 -1 0 0 -1 0]
[-1 0 0 -1 0 0 0 -1 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-3 -1 -1 -1 -1 -1 -1 -2 0]
[ 0 0 0 0 0 0 0 0 1]
[ 4 1 2 1 2 2 0 1 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-1 0 0 0 -1 -1 0 0 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-1 0 -1 0 0 -1 0 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-2 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 1 1 0 0 0 1 0 0]
[-1 0 -1 0 0 0 -1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 -1 0 0 0 0 -1 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 -1 -1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{2,12,12,12,18}
Orbit:
1
{@
Mod: ( 1 -1 0 0 0 -1 0 0 0),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0)
@}
Intersection Matrix:
[-1 2]
[ 2 -1]
Stabilizer Group Name:
C3*S3
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 1 0 0 0 1 0 0]
[-1 0 -1 0 0 0 -1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 -1 0 0 0 0 -1 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 -1 -1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 4 2 0 1 2 1 1 2 0]
[-2 -1 0 -1 -1 0 -1 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 4 1 2 1 2 2 0 1 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-1 0 0 0 -1 -1 0 0 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-1 0 -1 0 0 -1 0 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-2 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
2
{@
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 1 0 -1 -1 0 0 0 0 0),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: ( 1 0 0 0 0 -1 0 -1 0)
@}
Intersection Matrix:
[-1 1 1 2 1 1 0 1 0 0 0 0]
[ 1 -1 0 0 0 0 2 0 1 1 1 1]
[ 1 0 -1 0 0 0 1 0 1 1 1 2]
[ 2 0 0 -1 0 0 1 0 1 1 1 1]
[ 1 0 0 0 -1 0 1 0 1 1 2 1]
[ 1 0 0 0 0 -1 1 0 2 1 1 1]
[ 0 2 1 1 1 1 -1 1 0 0 0 0]
[ 1 0 0 0 0 0 1 -1 1 2 1 1]
[ 0 1 1 1 1 2 0 1 -1 0 0 0]
[ 0 1 1 1 1 1 0 2 0 -1 0 0]
[ 0 1 1 1 2 1 0 1 0 0 -1 0]
[ 0 1 2 1 1 1 0 1 0 0 0 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[ 4 1 2 1 2 2 0 1 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-1 0 0 0 -1 -1 0 0 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-1 0 -1 0 0 -1 0 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-2 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
3
{@
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 1 0 0 -1 0 -1 0 0 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0)
@}
Intersection Matrix:
[-1 0 0 0 0 0 0 0 0 0 1 0]
[ 0 -1 0 1 0 0 0 0 0 0 0 0]
[ 0 0 -1 0 0 1 0 0 0 0 0 0]
[ 0 1 0 -1 0 0 0 0 0 0 0 0]
[ 0 0 0 0 -1 0 0 0 0 1 0 0]
[ 0 0 1 0 0 -1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 -1 1 0 0 0 0]
[ 0 0 0 0 0 0 1 -1 0 0 0 0]
[ 0 0 0 0 0 0 0 0 -1 0 0 1]
[ 0 0 0 0 1 0 0 0 0 -1 0 0]
[ 1 0 0 0 0 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 0 0 1 0 0 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[ 4 1 2 1 2 2 0 1 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-1 0 0 0 -1 -1 0 0 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-1 0 -1 0 0 -1 0 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-2 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
4
{@
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: (0 0 0 1 0 0 0 0 0),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: (0 0 0 0 0 0 1 0 0),
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 1 -1 -1 0 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 0 0 1 0 0 0 0 0 0 0]
[ 0 -1 0 0 0 1 0 0 0 0 0 0]
[ 0 0 -1 0 0 0 1 0 0 0 0 0]
[ 0 0 0 -1 0 0 0 0 0 0 0 1]
[ 1 0 0 0 -1 0 0 0 0 0 0 0]
[ 0 1 0 0 0 -1 0 0 0 0 0 0]
[ 0 0 1 0 0 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 -1 0 1 0 0]
[ 0 0 0 0 0 0 0 0 -1 0 1 0]
[ 0 0 0 0 0 0 0 1 0 -1 0 0]
[ 0 0 0 0 0 0 0 0 1 0 -1 0]
[ 0 0 0 1 0 0 0 0 0 0 0 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[ 4 1 2 1 2 2 0 1 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-1 0 0 0 -1 -1 0 0 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-1 0 -1 0 0 -1 0 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-2 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
5
{@
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: (0 0 0 0 1 0 0 0 0),
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: (0 1 0 0 0 0 0 0 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0)
@}
Intersection Matrix:
[-1 0 0 0 1 1 0 1 0 0 0 1 1 1 0 1 1 2]
[ 0 -1 1 1 0 0 1 2 0 1 0 1 0 1 0 1 0 1]
[ 0 1 -1 0 1 2 0 0 1 1 0 0 0 1 0 1 1 1]
[ 0 1 0 -1 0 1 1 0 0 0 0 1 1 0 1 1 2 1]
[ 1 0 1 0 -1 0 2 1 0 1 0 1 0 0 1 1 1 0]
[ 1 0 2 1 0 -1 1 1 0 0 1 1 1 0 1 0 0 0]
[ 0 1 0 1 2 1 -1 0 1 0 1 0 1 1 0 0 0 1]
[ 1 2 0 0 1 1 0 -1 1 0 1 0 1 0 1 0 1 0]
[ 0 0 1 0 0 0 1 1 -1 0 1 2 1 1 0 0 1 1]
[ 0 1 1 0 1 0 0 0 0 -1 1 1 2 0 1 0 1 1]
[ 0 0 0 0 0 1 1 1 1 1 -1 0 0 0 1 2 1 1]
[ 1 1 0 1 1 1 0 0 2 1 0 -1 0 0 1 1 0 0]
[ 1 0 0 1 0 1 1 1 1 2 0 0 -1 1 0 1 0 0]
[ 1 1 1 0 0 0 1 0 1 0 0 0 1 -1 2 1 1 0]
[ 0 0 0 1 1 1 0 1 0 1 1 1 0 2 -1 0 0 1]
[ 1 1 1 1 1 0 0 0 0 0 2 1 1 1 0 -1 0 0]
[ 1 0 1 2 1 0 0 1 1 1 1 0 0 1 0 0 -1 0]
[ 2 1 1 1 0 0 1 0 1 1 1 0 0 0 1 0 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 4 2 0 1 2 1 1 2 0]
[-2 -1 0 -1 -1 0 -1 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
D6(11):C2*S4
order := 48,
length := 15120,
subgroup := MatrixGroup(9, Integer Ring) of order 2^4 * 3
Generators:
[ 6 2 3 1 2 2 2 3 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-3 -1 -1 -1 -1 -1 -1 -2 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 0 -1 0 -1 -1 -1 -1 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 5 2 3 1 1 2 1 2 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-1 0 -1 0 0 -1 0 0 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-1 -1 -1 0 0 0 0 0 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
[ 2 1 0 1 0 0 0 1 0]
[-1 0 0 -1 0 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 5 2 2 0 2 2 2 2 0]
[-2 0 -1 0 -1 -1 -1 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{2,6,12,12,24}
Orbit:
1
{@
Mod: ( 1 -1 0 0 0 -1 0 0 0),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0)
@}
Intersection Matrix:
[-1 2]
[ 2 -1]
Stabilizer Group Name:
C2*A4
MatrixGroup(9, Integer Ring)
Generators:
[ 5 2 2 0 2 2 2 2 0]
[-2 0 -1 0 -1 -1 -1 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 1 0 1 0 0 0 1 0]
[-1 0 0 -1 0 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
[ 5 2 3 1 1 2 1 2 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-1 0 -1 0 0 -1 0 0 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-1 -1 -1 0 0 0 0 0 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
2
{@
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 1 0 0 0 0 -1 0 -1 0),
Mod: ( 1 0 0 0 0 0 -1 -1 0)
@}
Intersection Matrix:
[-1 0 2 1 0 1]
[ 0 -1 1 0 1 2]
[ 2 1 -1 0 1 0]
[ 1 0 0 -1 2 1]
[ 0 1 1 2 -1 0]
[ 1 2 0 1 0 -1]
Stabilizer Group Name:
C2^3
MatrixGroup(9, Integer Ring)
Generators:
[ 5 2 2 0 2 2 2 2 0]
[-2 0 -1 0 -1 -1 -1 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 1 0 1 0 0 0 1 0]
[-1 0 0 -1 0 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
3
{@
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 1 0 0 -1 0 -1 0 0 0),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0)
@}
Intersection Matrix:
[-1 0 0 1 0 0 0 0 0 0 0 0]
[ 0 -1 0 0 0 0 0 0 0 0 1 0]
[ 0 0 -1 0 0 1 0 0 0 0 0 0]
[ 1 0 0 -1 0 0 0 0 0 0 0 0]
[ 0 0 0 0 -1 0 0 0 0 1 0 0]
[ 0 0 1 0 0 -1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 -1 0 1 0 0 0]
[ 0 0 0 0 0 0 0 -1 0 0 0 1]
[ 0 0 0 0 0 0 1 0 -1 0 0 0]
[ 0 0 0 0 1 0 0 0 0 -1 0 0]
[ 0 1 0 0 0 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 0 1 0 0 0 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 1 0 0 0 1 0]
[-1 0 0 -1 0 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
4
{@
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: (0 0 0 1 0 0 0 0 0),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: (0 0 0 0 0 0 1 0 0),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 1 -1 -1 0 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 0 0 1 0 0 0 0 0 0 0]
[ 0 -1 0 0 0 1 0 0 0 0 0 0]
[ 0 0 -1 0 0 0 0 0 0 0 0 1]
[ 0 0 0 -1 0 0 1 0 0 0 0 0]
[ 1 0 0 0 -1 0 0 0 0 0 0 0]
[ 0 1 0 0 0 -1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 -1 0 0 1 0]
[ 0 0 0 0 0 0 0 0 -1 1 0 0]
[ 0 0 0 0 0 0 0 0 1 -1 0 0]
[ 0 0 0 0 0 0 0 1 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0 0 0 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 5 2 2 0 2 2 2 2 0]
[-2 0 -1 0 -1 -1 -1 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 1 0 1 0 0 0 1 0]
[-1 0 0 -1 0 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
5
{@
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: (0 0 0 0 1 0 0 0 0),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 1 0 -1 -1 0 0 0 0 0),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: (0 1 0 0 0 0 0 0 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0)
@}
Intersection Matrix:
[-1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 0 0 0 1 1 2 1]
[ 0 -1 0 1 1 1 0 2 0 1 1 1 0 1 1 0 1 0 0 0 1 0 1 0]
[ 0 0 -1 0 0 0 1 1 0 0 2 1 0 1 1 0 1 0 0 1 1 1 1 1]
[ 0 1 0 -1 0 1 2 0 1 0 1 1 0 0 0 0 1 0 1 0 1 1 1 1]
[ 0 1 0 0 -1 0 1 0 0 0 1 0 0 1 0 1 0 1 1 1 1 2 1 1]
[ 1 1 0 1 0 -1 0 0 0 0 1 0 1 1 1 1 0 1 0 2 0 1 0 1]
[ 1 0 1 2 1 0 -1 1 0 1 0 0 1 1 1 1 0 1 0 1 0 0 0 0]
[ 1 2 1 0 0 0 1 -1 1 0 0 0 1 0 0 1 0 1 1 1 0 1 0 1]
[ 0 0 0 1 0 0 0 1 -1 1 1 0 1 2 1 1 1 0 0 1 0 1 1 0]
[ 0 1 0 0 0 0 1 0 1 -1 1 0 0 0 1 1 0 1 0 1 1 1 1 2]
[ 1 1 2 1 1 1 0 0 1 1 -1 0 1 0 0 1 0 1 1 0 0 0 0 0]
[ 0 1 1 1 0 0 0 0 0 0 0 -1 1 1 1 2 0 1 0 1 0 1 1 1]
[ 0 0 0 0 0 1 1 1 1 0 1 1 -1 0 0 0 0 1 1 0 2 1 1 1]
[ 1 1 1 0 1 1 1 0 2 0 0 1 0 -1 0 0 0 1 1 0 1 0 0 1]
[ 1 1 1 0 0 1 1 0 1 1 0 1 0 0 -1 0 0 1 2 0 1 1 0 0]
[ 1 0 0 0 1 1 1 1 1 1 1 2 0 0 0 -1 1 0 1 0 1 0 0 0]
[ 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 -1 2 1 1 1 1 0 1]
[ 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 0 2 -1 0 0 0 0 1 0]
[ 0 0 0 1 1 0 0 1 0 0 1 0 1 1 2 1 1 0 -1 1 0 0 1 1]
[ 0 0 1 0 1 2 1 1 1 1 0 1 0 0 0 0 1 0 1 -1 1 0 1 0]
[ 1 1 1 1 1 0 0 0 0 1 0 0 2 1 1 1 1 0 0 1 -1 0 0 0]
[ 1 0 1 1 2 1 0 1 1 1 0 1 1 0 1 0 1 0 0 0 0 -1 0 0]
[ 2 1 1 1 1 0 0 0 1 1 0 1 1 0 0 0 0 1 1 1 0 0 -1 0]
[ 1 0 1 1 1 1 0 1 0 2 0 1 1 1 0 0 1 0 1 0 0 0 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
D6(12):C2*S4
order := 48,
length := 15120,
subgroup := MatrixGroup(9, Integer Ring) of order 2^4 * 3
Generators:
[ 2 0 0 0 1 1 1 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 1 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[-1 0 0 0 -1 -1 0 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[-1 0 0 0 0 -1 -1 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 5 1 2 2 3 1 1 2 0]
[-2 0 -1 -1 -1 0 -1 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
[-1 0 -1 0 -1 0 0 0 0]
[-1 0 0 -1 -1 0 0 0 0]
[-2 -1 -1 -1 -1 0 0 -1 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 1 0 0 1 0 1 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 -1 0 0 0 0 -1 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
[1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
[1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1]>
Orbit type:{6,6,8,12,12,12}
Orbit:
1
{@
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: (0 0 0 0 1 0 0 0 0),
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 1 0 0 0 -1 -1 0 0 0)
@}
Intersection Matrix:
[-1 1 1 1 1 0]
[ 1 -1 0 1 1 1]
[ 1 0 -1 1 1 1]
[ 1 1 1 -1 0 1]
[ 1 1 1 0 -1 1]
[ 0 1 1 1 1 -1]
Stabilizer Group Name:
D4
MatrixGroup(9, Integer Ring)
Generators:
[ 6 1 2 3 3 2 2 2 0]
[-1 0 0 -1 -1 0 0 0 0]
[-2 0 0 -1 -1 -1 -1 -1 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-3 -1 -1 -2 -1 -1 -1 -1 0]
[-2 0 -1 -1 -1 0 -1 -1 0]
[-2 0 -1 -1 -1 -1 -1 0 0]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 1 0 0 1 0 1 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 -1 0 0 0 0 -1 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
[1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1]
2
{@
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: (0 0 0 1 0 0 0 0 0)
@}
Intersection Matrix:
[-1 1 0 1 1 1]
[ 1 -1 1 1 0 1]
[ 0 1 -1 1 1 1]
[ 1 1 1 -1 1 0]
[ 1 0 1 1 -1 1]
[ 1 1 1 0 1 -1]
Stabilizer Group Name:
D4
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
[ 4 1 1 2 0 1 2 2 0]
[-1 0 0 -1 0 0 0 -1 0]
[-1 0 0 -1 0 0 -1 0 0]
[-2 -1 0 -1 0 -1 -1 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[-2 0 -1 -1 0 -1 -1 -1 0]
[-2 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1]
3
{@
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 1 0 -1 -1 0 0 0 0 0),
Mod: ( 1 0 0 -1 0 -1 0 0 0),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 1 0 0 0 0 -1 0 -1 0)
@}
Intersection Matrix:
[-1 0 1 1 2 1 0 0]
[ 0 -1 2 0 1 0 1 1]
[ 1 2 -1 1 0 1 0 0]
[ 1 0 1 -1 0 1 0 2]
[ 2 1 0 0 -1 0 1 1]
[ 1 0 1 1 0 -1 2 0]
[ 0 1 0 0 1 2 -1 1]
[ 0 1 0 2 1 0 1 -1]
Stabilizer Group Name:
S3
MatrixGroup(9, Integer Ring)
Generators:
[ 5 1 2 2 3 1 1 2 0]
[-2 0 -1 -1 -1 0 -1 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
[-1 0 -1 0 -1 0 0 0 0]
[-1 0 0 -1 -1 0 0 0 0]
[-2 -1 -1 -1 -1 0 0 -1 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 6 1 2 3 3 2 2 2 0]
[-1 0 0 -1 -1 0 0 0 0]
[-2 0 0 -1 -1 -1 -1 -1 0]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
[-3 -1 -1 -2 -1 -1 -1 -1 0]
[-2 0 -1 -1 -1 0 -1 -1 0]
[-2 0 -1 -1 -1 -1 -1 0 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
4
{@
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: (0 0 0 0 0 0 1 0 0),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0)
@}
Intersection Matrix:
[-1 0 1 1 1 2 0 0 0 1 1 0]
[ 0 -1 2 1 1 1 0 0 0 1 1 0]
[ 1 2 -1 0 0 0 1 1 1 0 0 1]
[ 1 1 0 -1 0 0 1 1 2 0 0 1]
[ 1 1 0 0 -1 0 2 1 1 0 0 1]
[ 2 1 0 0 0 -1 1 1 1 0 0 1]
[ 0 0 1 1 2 1 -1 0 0 1 1 0]
[ 0 0 1 1 1 1 0 -1 0 1 2 0]
[ 0 0 1 2 1 1 0 0 -1 1 1 0]
[ 1 1 0 0 0 0 1 1 1 -1 0 2]
[ 1 1 0 0 0 0 1 2 1 0 -1 1]
[ 0 0 1 1 1 1 0 0 0 2 1 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 0 1 0 1 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 -1 0 0 0 0 -1 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
[1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1]
5
{@
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: (0 1 0 0 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 0 0 1 0 0 0 0 0 0 0]
[ 0 -1 1 0 0 0 0 0 0 0 0 0]
[ 0 1 -1 0 0 0 0 0 0 0 0 0]
[ 0 0 0 -1 0 0 0 0 0 1 0 0]
[ 1 0 0 0 -1 0 0 0 0 0 0 0]
[ 0 0 0 0 0 -1 0 1 0 0 0 0]
[ 0 0 0 0 0 0 -1 0 0 0 1 0]
[ 0 0 0 0 0 1 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 0 0 -1 0 0 1]
[ 0 0 0 1 0 0 0 0 0 -1 0 0]
[ 0 0 0 0 0 0 1 0 0 0 -1 0]
[ 0 0 0 0 0 0 0 0 1 0 0 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
[ 2 1 0 0 1 0 1 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 -1 0 0 0 0 -1 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
6
{@
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: ( 1 -1 -1 0 0 0 0 0 0),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 1 -1 0 0 0 -1 0 0 0)
@}
Intersection Matrix:
[-1 0 0 0 0 0 0 0 0 0 1 0]
[ 0 -1 0 0 0 0 0 0 0 1 0 0]
[ 0 0 -1 0 1 0 0 0 0 0 0 0]
[ 0 0 0 -1 0 0 0 1 0 0 0 0]
[ 0 0 1 0 -1 0 0 0 0 0 0 0]
[ 0 0 0 0 0 -1 0 0 1 0 0 0]
[ 0 0 0 0 0 0 -1 0 0 0 0 1]
[ 0 0 0 1 0 0 0 -1 0 0 0 0]
[ 0 0 0 0 0 1 0 0 -1 0 0 0]
[ 0 1 0 0 0 0 0 0 0 -1 0 0]
[ 1 0 0 0 0 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0 0 0 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
[1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 1]
D6(13):S5
order := 120,
length := 6048,
subgroup := MatrixGroup(9, Integer Ring) of order 2^3 * 3 * 5
Generators:
[ 2 0 0 1 0 0 1 1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 0 0 1 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 0 -1 0 0 0 -1 0]
[-1 0 0 -1 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 4 1 3 1 1 1 1 1 0]
[-1 0 -1 0 0 -1 0 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[-1 0 -1 0 0 0 -1 0 0]
[-1 0 -1 0 0 0 0 -1 0]
[-1 -1 -1 0 0 0 0 0 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-1 0 -1 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{2,12,12,30}
Orbit:
1
{@
Mod: ( 1 -1 0 0 0 -1 0 0 0),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0)
@}
Intersection Matrix:
[-1 2]
[ 2 -1]
Stabilizer Group Name:
A5
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
[ 4 1 1 0 1 2 2 2 0]
[-2 0 -1 0 -1 -1 -1 -1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[-1 0 0 0 0 -1 -1 0 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 5 2 2 1 1 2 3 1 0]
[-3 -1 -1 -1 -1 -1 -2 -1 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[-1 -1 0 0 0 0 -1 0 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-1 0 -1 0 0 0 -1 0 0]
[-1 0 0 0 0 -1 -1 0 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
2
{@
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: (0 0 0 0 1 0 0 0 0),
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 1 -1 -1 0 0 0 0 0 0),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: (0 0 0 1 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 0 0 0 0 0 0 0 0 1 0]
[ 0 -1 0 0 0 0 1 0 0 0 0 0]
[ 0 0 -1 0 0 1 0 0 0 0 0 0]
[ 0 0 0 -1 1 0 0 0 0 0 0 0]
[ 0 0 0 1 -1 0 0 0 0 0 0 0]
[ 0 0 1 0 0 -1 0 0 0 0 0 0]
[ 0 1 0 0 0 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 -1 0 1 0 0]
[ 0 0 0 0 0 0 0 0 -1 0 0 1]
[ 0 0 0 0 0 0 0 1 0 -1 0 0]
[ 1 0 0 0 0 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 0 0 1 0 0 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
[ 3 1 2 1 0 1 0 1 0]
[-1 0 -1 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 -1 0 0 0 0 0 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[-1 0 -1 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
3
{@
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: ( 1 0 0 -1 0 -1 0 0 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0)
@}
Intersection Matrix:
[-1 0 0 0 0 0 0 0 0 1 0 0]
[ 0 -1 0 1 0 0 0 0 0 0 0 0]
[ 0 0 -1 0 0 0 0 0 1 0 0 0]
[ 0 1 0 -1 0 0 0 0 0 0 0 0]
[ 0 0 0 0 -1 0 0 0 0 0 0 1]
[ 0 0 0 0 0 -1 0 1 0 0 0 0]
[ 0 0 0 0 0 0 -1 0 0 0 1 0]
[ 0 0 0 0 0 1 0 -1 0 0 0 0]
[ 0 0 1 0 0 0 0 0 -1 0 0 0]
[ 1 0 0 0 0 0 0 0 0 -1 0 0]
[ 0 0 0 0 0 0 1 0 0 0 -1 0]
[ 0 0 0 0 1 0 0 0 0 0 0 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[ 4 1 1 0 1 2 2 2 0]
[-2 0 -1 0 -1 -1 -1 -1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[-1 0 0 0 0 -1 -1 0 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 3 1 0 0 1 1 2 1 0]
[-1 0 0 0 -1 0 -1 0 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 -1 0 0 0 0 -1 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-1 0 0 0 0 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
4
{@
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: ( 1 0 -1 -1 0 0 0 0 0),
Mod: ( 1 0 0 0 0 -1 0 -1 0),
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: (0 1 0 0 0 0 0 0 0),
Mod: (0 0 0 0 0 0 1 0 0)
@}
Intersection Matrix:
[-1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 2 0 0 0]
[ 1 -1 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 2 1]
[ 0 1 -1 0 0 1 2 0 0 1 0 1 0 0 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 0]
[ 1 1 0 -1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 1 0 2 0 0 1 0 0 1 0 1]
[ 1 1 0 0 -1 1 1 1 0 1 0 1 1 1 0 0 0 0 1 2 0 1 1 0 0 0 0 1 0 1]
[ 1 0 1 1 1 -1 0 0 0 1 0 1 1 0 1 1 1 1 1 0 2 0 0 1 0 0 0 0 1 0]
[ 1 0 2 1 1 0 -1 1 1 0 1 0 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 1]
[ 1 0 0 0 1 0 1 -1 0 1 1 1 0 0 2 1 1 1 0 0 1 1 0 0 1 0 0 1 1 0]
[ 1 0 0 1 0 0 1 0 -1 2 0 1 1 1 1 0 1 0 1 1 1 0 1 0 0 0 0 1 1 0]
[ 0 1 1 0 1 1 0 1 2 -1 1 0 0 0 0 1 0 1 0 0 0 1 0 1 1 1 1 0 0 1]
[ 0 1 0 1 0 0 1 1 0 1 -1 1 1 0 0 0 1 1 2 1 1 0 1 1 0 0 1 0 0 0]
[ 0 1 1 1 1 1 0 1 1 0 1 -1 1 1 0 1 1 0 0 0 0 0 0 0 0 2 1 1 0 0]
[ 0 0 0 0 1 1 1 0 1 0 1 1 -1 0 1 0 0 1 0 0 0 1 1 1 2 0 1 0 1 1]
[ 0 1 0 0 1 0 1 0 1 0 0 1 0 -1 1 1 1 2 1 0 1 1 0 1 1 0 1 0 0 0]
[ 0 1 1 1 0 1 0 2 1 0 0 0 1 1 -1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1]
[ 0 0 0 1 0 1 1 1 0 1 0 1 0 1 0 -1 0 0 1 1 0 0 2 1 1 0 1 0 1 1]
[ 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 -1 0 0 1 0 1 1 1 1 0 0 0 1 2]
[ 1 0 1 1 0 1 0 1 0 1 1 0 1 2 0 0 0 -1 0 1 0 0 1 0 0 1 0 1 1 1]
[ 1 0 1 0 1 1 0 0 1 0 2 0 0 1 1 1 0 0 -1 0 0 1 0 0 1 1 0 1 1 1]
[ 0 0 1 1 2 0 0 0 1 0 1 0 0 0 1 1 1 1 0 -1 1 0 0 1 1 1 1 0 1 0]
[ 0 1 0 0 0 2 1 1 1 0 1 0 0 1 0 0 0 0 0 1 -1 1 1 0 1 1 1 1 0 1]
[ 0 0 1 2 1 0 0 1 0 1 0 0 1 1 0 0 1 0 1 0 1 -1 1 1 0 1 1 0 1 0]
[ 1 1 1 0 1 0 0 0 1 0 1 0 1 0 1 2 1 1 0 0 1 1 -1 0 0 1 0 1 0 0]
[ 1 1 0 0 0 1 1 0 0 1 1 0 1 1 1 1 1 0 0 1 0 1 0 -1 0 1 0 2 0 0]
[ 1 1 1 1 0 0 0 1 0 1 0 0 2 1 0 1 1 0 1 1 1 0 0 0 -1 1 0 1 0 0]
[ 1 0 0 0 0 0 1 0 0 1 0 2 0 0 1 0 0 1 1 1 1 1 1 1 1 -1 0 0 1 1]
[ 2 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 -1 1 1 1]
[ 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0 1 0 1 2 1 0 1 -1 1 1]
[ 0 2 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 -1 0]
[ 0 1 0 1 1 0 1 0 0 1 0 0 1 0 1 1 2 1 1 0 1 0 0 0 0 1 1 1 0 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 5 2 2 2 0 2 2 2 0]
[-2 0 -1 -1 0 -1 -1 -1 0]
[-2 -1 0 -1 0 -1 -1 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[-2 -1 -1 -1 0 0 -1 -1 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 1 1 0 1 0 0 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 -1 -1 0 0 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 0 0 0 0 0 0 1]
D6(14):S5
order := 120,
length := 6048,
subgroup := MatrixGroup(9, Integer Ring) of order 2^3 * 3 * 5
Generators:
[ 6 1 2 3 2 2 2 3 0]
[-1 0 0 -1 0 0 0 -1 0]
[-2 0 0 -1 -1 -1 -1 -1 0]
[-3 -1 -1 -1 -1 -1 -1 -2 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-2 0 -1 -1 -1 0 -1 -1 0]
[-2 0 -1 -1 0 -1 -1 -1 0]
[-3 -1 -1 -2 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 4 1 1 2 2 1 2 0 0]
[-1 0 0 -1 -1 0 0 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[-2 -1 -1 -1 -1 0 -1 0 0]
[ 0 0 0 0 0 0 0 1 0]
[-1 0 0 -1 0 0 -1 0 0]
[-2 0 -1 -1 -1 -1 -1 0 0]
[-2 -1 0 -1 -1 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{10,10,12,12,12}
Orbit:
1
{@
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 1 0 -1 -1 0 0 0 0 0),
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 1 0 0 -1 0 -1 0 0 0),
Mod: (0 0 0 1 0 0 0 0 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0)
@}
Intersection Matrix:
[-1 1 1 0 1 1 0 0 1 1]
[ 1 -1 1 1 0 1 1 0 1 0]
[ 1 1 -1 0 0 0 1 1 1 1]
[ 0 1 0 -1 1 1 1 1 1 0]
[ 1 0 0 1 -1 1 0 1 1 1]
[ 1 1 0 1 1 -1 1 0 0 1]
[ 0 1 1 1 0 1 -1 1 0 1]
[ 0 0 1 1 1 0 1 -1 1 1]
[ 1 1 1 1 1 0 0 1 -1 0]
[ 1 0 1 0 1 1 1 1 0 -1]
Stabilizer Group Name:
D6
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 2 0 1 1 0]
[-1 0 0 0 -1 0 -1 0 0]
[-1 0 0 0 -1 0 0 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 5 2 1 1 3 1 2 2 0]
[-1 0 0 0 -1 0 -1 0 0]
[-1 0 0 0 -1 0 0 -1 0]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[-2 -1 0 -1 -1 0 -1 -1 0]
[-1 -1 0 0 -1 0 0 0 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 0 0 0 0 1 1 1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 1 0 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[-1 0 0 0 0 -1 -1 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
2
{@
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 1 0 0 0 0 -1 0 -1 0),
Mod: (0 0 0 0 1 0 0 0 0)
@}
Intersection Matrix:
[-1 0 1 1 1 1 0 1 0 1]
[ 0 -1 1 1 0 0 1 1 1 1]
[ 1 1 -1 1 1 0 1 0 0 1]
[ 1 1 1 -1 1 0 0 1 1 0]
[ 1 0 1 1 -1 1 1 0 1 0]
[ 1 0 0 0 1 -1 1 1 1 1]
[ 0 1 1 0 1 1 -1 0 1 1]
[ 1 1 0 1 0 1 0 -1 1 1]
[ 0 1 0 1 1 1 1 1 -1 0]
[ 1 1 1 0 0 1 1 1 0 -1]
Stabilizer Group Name:
D6
MatrixGroup(9, Integer Ring)
Generators:
[ 5 2 1 3 1 1 2 2 0]
[-1 0 0 -1 0 0 -1 0 0]
[-2 -1 0 -1 -1 0 -1 -1 0]
[-2 -1 0 -1 0 -1 -1 -1 0]
[-3 -1 -1 -2 -1 -1 -1 -1 0]
[-1 0 0 -1 0 0 0 -1 0]
[-1 -1 0 -1 0 0 0 0 0]
[-2 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 6 1 2 3 2 2 2 3 0]
[-1 0 0 -1 0 0 0 -1 0]
[-2 0 0 -1 -1 -1 -1 -1 0]
[-3 -1 -1 -1 -1 -1 -1 -2 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-2 0 -1 -1 -1 0 -1 -1 0]
[-2 0 -1 -1 0 -1 -1 -1 0]
[-3 -1 -1 -2 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 3 0 1 1 2 1 0 1 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 -1 0 0 -1 0]
[-1 0 0 0 -1 -1 0 0 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-1 0 0 -1 -1 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
3
{@
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: (0 0 0 0 0 0 1 0 0),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0)
@}
Intersection Matrix:
[-1 1 1 0 2 1 0 0 0 1 1 0]
[ 1 -1 0 2 0 0 1 1 1 0 0 1]
[ 1 0 -1 1 0 0 1 1 2 0 0 1]
[ 0 2 1 -1 1 1 0 0 0 1 1 0]
[ 2 0 0 1 -1 0 1 1 1 0 0 1]
[ 1 0 0 1 0 -1 2 1 1 0 0 1]
[ 0 1 1 0 1 2 -1 0 0 1 1 0]
[ 0 1 1 0 1 1 0 -1 0 1 2 0]
[ 0 1 2 0 1 1 0 0 -1 1 1 0]
[ 1 0 0 1 0 0 1 1 1 -1 0 2]
[ 1 0 0 1 0 0 1 2 1 0 -1 1]
[ 0 1 1 0 1 1 0 0 0 2 1 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[ 2 0 1 1 1 0 0 0 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 -1 -1 0 0 0 0]
[-1 0 -1 -1 0 0 0 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 3 1 1 1 0 0 1 2 0]
[-1 0 0 0 0 0 -1 -1 0]
[-1 0 0 -1 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 -1 -1 0 0 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
4
{@
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: (0 1 0 0 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 0 0 1 0 0 0 0 0 0 0]
[ 0 -1 0 1 0 0 0 0 0 0 0 0]
[ 0 0 -1 0 0 0 0 0 1 0 0 0]
[ 0 1 0 -1 0 0 0 0 0 0 0 0]
[ 1 0 0 0 -1 0 0 0 0 0 0 0]
[ 0 0 0 0 0 -1 0 1 0 0 0 0]
[ 0 0 0 0 0 0 -1 0 0 0 1 0]
[ 0 0 0 0 0 1 0 -1 0 0 0 0]
[ 0 0 1 0 0 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 0 -1 0 1]
[ 0 0 0 0 0 0 1 0 0 0 -1 0]
[ 0 0 0 0 0 0 0 0 0 1 0 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1]
[ 6 2 1 3 3 2 2 2 0]
[-2 0 0 -1 -1 -1 -1 -1 0]
[-2 -1 0 -1 -1 0 -1 -1 0]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
[-2 -1 0 -1 -1 -1 -1 0 0]
[-1 0 0 -1 -1 0 0 0 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[-3 -1 -1 -2 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
5
{@
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: ( 1 -1 -1 0 0 0 0 0 0),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 1 -1 0 0 0 -1 0 0 0)
@}
Intersection Matrix:
[-1 0 0 0 0 0 0 0 0 0 1 0]
[ 0 -1 0 0 0 0 0 0 0 1 0 0]
[ 0 0 -1 0 1 0 0 0 0 0 0 0]
[ 0 0 0 -1 0 0 0 1 0 0 0 0]
[ 0 0 1 0 -1 0 0 0 0 0 0 0]
[ 0 0 0 0 0 -1 0 0 1 0 0 0]
[ 0 0 0 0 0 0 -1 0 0 0 0 1]
[ 0 0 0 1 0 0 0 -1 0 0 0 0]
[ 0 0 0 0 0 1 0 0 -1 0 0 0]
[ 0 1 0 0 0 0 0 0 0 -1 0 0]
[ 1 0 0 0 0 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0 0 0 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[ 5 2 1 3 2 1 2 1 0]
[-1 0 0 -1 0 0 -1 0 0]
[-2 -1 0 -1 -1 0 -1 -1 0]
[-2 -1 -1 -1 -1 0 -1 0 0]
[-3 -1 -1 -2 -1 -1 -1 -1 0]
[-1 0 0 -1 -1 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[-2 -1 0 -1 -1 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 3 0 1 1 2 1 0 1 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 -1 0 0 -1 0]
[-1 0 0 0 -1 -1 0 0 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-1 0 0 -1 -1 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]