dP2(1):D7
order := 14,
length := 34560,
subgroup := MatrixGroup(9, Integer Ring) of order 2 * 7
Generators:
[ 5 2 1 3 2 2 1 1 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[-1 0 0 -1 -1 0 0 0 0]
[-3 -1 -1 -2 -1 -1 -1 -1 0]
[-2 -1 -1 -1 -1 -1 0 0 0]
[-2 -1 0 -1 -1 -1 -1 0 0]
[-1 0 0 -1 0 -1 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 6 3 2 2 1 3 2 2 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-1 -1 0 0 0 -1 0 0 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[-2 -1 0 -1 0 -1 -1 -1 0]
[-3 -1 -1 -1 -1 -2 -1 -1 0]
[-3 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{14,14,14,14}
Orbit:
1
{@
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0),
Mod: ( 1 -1 0 0 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 0 0 0 0 -1 -1 0),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 2 -1 -1 -1 -1 -1 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 0 1 1 0 0 1 1 1 0 0 2]
[ 0 -1 2 1 1 1 1 0 0 1 0 0 0 1]
[ 1 2 -1 0 0 0 0 1 1 0 1 1 1 0]
[ 0 1 0 -1 1 1 0 0 1 0 2 1 0 1]
[ 1 1 0 1 -1 0 1 2 0 1 0 0 1 0]
[ 1 1 0 1 0 -1 0 1 1 0 0 1 2 0]
[ 0 1 0 0 1 0 -1 0 2 0 1 1 1 1]
[ 0 0 1 0 2 1 0 -1 1 0 1 1 0 1]
[ 1 0 1 1 0 1 2 1 -1 1 0 0 0 0]
[ 1 1 0 0 1 0 0 0 1 -1 1 2 1 0]
[ 1 0 1 2 0 0 1 1 0 1 -1 0 1 0]
[ 0 0 1 1 0 1 1 1 0 2 0 -1 0 1]
[ 0 0 1 0 1 2 1 0 0 1 1 0 -1 1]
[ 2 1 0 1 0 0 1 1 0 0 0 1 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
2
{@
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: ( 1 0 0 0 0 -1 -1 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 -1 0 0 0 0 0 0),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: (0 1 0 0 0 0 0 0 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: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0)
@}
Intersection Matrix:
[-1 1 1 0 0 0 1 2 1 0 1 0 0 1]
[ 1 -1 1 0 1 1 0 0 0 1 1 0 2 0]
[ 1 1 -1 2 0 1 0 0 0 1 0 1 0 1]
[ 0 0 2 -1 1 0 1 1 1 0 1 0 1 0]
[ 0 1 0 1 -1 0 1 1 0 1 0 1 0 2]
[ 0 1 1 0 0 -1 2 1 1 0 0 1 0 1]
[ 1 0 0 1 1 2 -1 0 0 1 1 0 1 0]
[ 2 0 0 1 1 1 0 -1 0 1 0 1 1 0]
[ 1 0 0 1 0 1 0 0 -1 2 0 1 1 1]
[ 0 1 1 0 1 0 1 1 2 -1 1 0 0 0]
[ 1 1 0 1 0 0 1 0 0 1 -1 2 0 1]
[ 0 0 1 0 1 1 0 1 1 0 2 -1 1 0]
[ 0 2 0 1 0 0 1 1 1 0 0 1 -1 1]
[ 1 0 1 0 2 1 0 0 1 0 1 0 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
3
{@
Mod: (0 0 0 0 0 0 1 0 0),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: (0 0 0 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: ( 2 -1 0 -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)
@}
Intersection Matrix:
[-1 1 0 1 0 1 0 1 0 1 0 1 2 0]
[ 1 -1 0 0 2 1 1 1 1 1 0 0 0 0]
[ 0 0 -1 1 1 1 1 2 0 1 0 0 1 0]
[ 1 0 1 -1 1 1 1 0 2 0 1 0 0 0]
[ 0 2 1 1 -1 0 0 0 0 0 1 1 1 1]
[ 1 1 1 1 0 -1 0 0 0 0 1 1 0 2]
[ 0 1 1 1 0 0 -1 0 0 1 0 2 1 1]
[ 1 1 2 0 0 0 0 -1 1 0 1 1 0 1]
[ 0 1 0 2 0 0 0 1 -1 1 0 1 1 1]
[ 1 1 1 0 0 0 1 0 1 -1 2 0 0 1]
[ 0 0 0 1 1 1 0 1 0 2 -1 1 1 0]
[ 1 0 0 0 1 1 2 1 1 0 1 -1 0 0]
[ 2 0 1 0 1 0 1 0 1 0 1 0 -1 1]
[ 0 0 0 0 1 2 1 1 1 1 0 0 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
4
{@
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 1 0 -1 -1 0 0 0 0 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0),
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: (0 0 0 1 0 0 0 0 0),
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 1 -1 0 0 0 -1 0 0 0)
@}
Intersection Matrix:
[-1 0 1 1 0 0 0 0 0 1 2 1 1 1]
[ 0 -1 1 1 0 0 0 0 0 1 1 2 1 1]
[ 1 1 -1 0 1 2 1 1 1 0 0 0 0 0]
[ 1 1 0 -1 2 1 1 1 1 0 0 0 0 0]
[ 0 0 1 2 -1 0 0 0 0 1 1 1 1 1]
[ 0 0 2 1 0 -1 0 0 0 1 1 1 1 1]
[ 0 0 1 1 0 0 -1 0 0 1 1 1 2 1]
[ 0 0 1 1 0 0 0 -1 0 2 1 1 1 1]
[ 0 0 1 1 0 0 0 0 -1 1 1 1 1 2]
[ 1 1 0 0 1 1 1 2 1 -1 0 0 0 0]
[ 2 1 0 0 1 1 1 1 1 0 -1 0 0 0]
[ 1 2 0 0 1 1 1 1 1 0 0 -1 0 0]
[ 1 1 0 0 1 1 2 1 1 0 0 0 -1 0]
[ 1 1 0 0 1 1 1 1 2 0 0 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
dP2(2):F7
order := 42,
length := 34560,
subgroup := MatrixGroup(9, Integer Ring) of order 2 * 3 * 7
Generators:
[ 3 0 1 0 1 1 1 2 0]
[-1 0 0 0 0 0 -1 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 0 -1 0 0 0 0 -1 0]
[ 0 1 0 0 0 0 0 0 0]
[-2 0 -1 0 -1 -1 -1 -1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 5 2 1 3 2 2 1 1 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[-1 0 0 -1 -1 0 0 0 0]
[-3 -1 -1 -2 -1 -1 -1 -1 0]
[-2 -1 -1 -1 -1 -1 0 0 0]
[-2 -1 0 -1 -1 -1 -1 0 0]
[-1 0 0 -1 0 -1 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 6 3 2 2 1 3 2 2 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-1 -1 0 0 0 -1 0 0 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[-2 -1 0 -1 0 -1 -1 -1 0]
[-3 -1 -1 -1 -1 -2 -1 -1 0]
[-3 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{14,42}
Orbit:
1
{@
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 1 0 -1 -1 0 0 0 0 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0),
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: (0 0 0 1 0 0 0 0 0),
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 1 -1 0 0 0 -1 0 0 0)
@}
Intersection Matrix:
[-1 0 1 1 0 0 0 0 0 1 2 1 1 1]
[ 0 -1 1 1 0 0 0 0 0 1 1 2 1 1]
[ 1 1 -1 0 1 2 1 1 1 0 0 0 0 0]
[ 1 1 0 -1 2 1 1 1 1 0 0 0 0 0]
[ 0 0 1 2 -1 0 0 0 0 1 1 1 1 1]
[ 0 0 2 1 0 -1 0 0 0 1 1 1 1 1]
[ 0 0 1 1 0 0 -1 0 0 1 1 1 2 1]
[ 0 0 1 1 0 0 0 -1 0 2 1 1 1 1]
[ 0 0 1 1 0 0 0 0 -1 1 1 1 1 2]
[ 1 1 0 0 1 1 1 2 1 -1 0 0 0 0]
[ 2 1 0 0 1 1 1 1 1 0 -1 0 0 0]
[ 1 2 0 0 1 1 1 1 1 0 0 -1 0 0]
[ 1 1 0 0 1 1 2 1 1 0 0 0 -1 0]
[ 1 1 0 0 1 1 1 1 2 0 0 0 0 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[ 5 1 1 2 3 2 1 2 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[-1 0 0 0 -1 -1 0 0 0]
[-1 0 0 -1 -1 0 0 0 0]
[-2 0 0 -1 -1 -1 -1 -1 0]
[-1 0 0 0 -1 0 0 -1 0]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
2
{@
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: (0 0 0 0 1 0 0 0 0),
Mod: ( 1 -1 -1 0 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 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 1 -1 0 -1 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 0 0 -1 0 -1 0),
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 2 -1 -1 0 0 -1 -1 -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: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: (0 1 0 0 0 0 0 0 0),
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: ( 1 0 0 -1 0 -1 0 0 0),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: (0 0 0 0 0 0 1 0 0)
@}
Intersection Matrix:
[-1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 2 1]
[ 1 -1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 0 1 0 0 1 0 1 1 1 0 1 1 0 0 2 0 1 0 1 0 1]
[ 1 0 -1 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 1 0 1 0 1 0 0 0 1 1 1 2 1 0 0 1 0 0 0 1 0 0]
[ 1 1 1 -1 0 1 1 0 1 0 0 0 1 1 0 0 1 1 1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 2 1 1 0 0 1]
[ 1 0 1 0 -1 0 1 1 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 1 0 1 0 1 1 0 0 0 1 0 1 1 1 2 0 1 0 1]
[ 1 0 0 1 0 -1 0 0 0 1 1 2 0 1 0 1 1 1 0 0 1 0 1 0 1 1 0 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0]
[ 0 1 0 1 1 0 -1 0 1 2 1 1 1 1 0 1 1 0 1 0 1 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 0 0 0 1 1 0]
[ 1 1 0 0 1 0 0 -1 1 1 0 1 1 1 0 1 1 1 0 0 1 0 1 0 2 0 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0]
[ 0 0 1 1 0 0 1 1 -1 0 1 1 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 2 0 0 0 0 0 1 1 1 0 1 1 0 1 1]
[ 1 0 1 0 0 1 2 1 0 -1 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1]
[ 1 1 1 0 1 1 1 0 1 0 -1 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 2 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0]
[ 0 1 1 0 1 2 1 1 1 0 0 -1 1 0 1 0 0 0 1 1 0 1 0 1 0 0 1 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1]
[ 1 0 1 1 0 0 1 1 0 0 0 1 -1 0 0 0 1 1 0 1 1 1 1 1 0 2 1 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0]
[ 1 0 0 1 1 1 1 1 1 0 0 0 0 -1 1 0 0 0 0 2 1 1 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 0 0 1 0 0]
[ 1 1 1 0 0 0 0 0 1 1 0 1 0 1 -1 0 2 1 1 0 1 0 0 1 1 1 1 0 1 0 0 0 0 1 1 0 1 1 0 1 0 0]
[ 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 -1 1 0 1 1 1 1 0 2 0 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0]
[ 0 0 0 1 1 1 1 1 0 0 1 0 1 0 2 1 -1 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0 1 0 1 1]
[ 0 1 0 1 1 1 0 1 1 1 1 0 1 0 1 0 0 -1 1 1 1 1 0 1 0 0 0 0 0 0 2 1 1 0 1 0 0 0 0 1 1 0]
[ 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 1 0 1 -1 1 1 1 2 0 1 1 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0 0]
[ 0 1 1 0 0 0 0 0 0 1 1 1 1 2 0 1 1 1 1 -1 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 1]
[ 0 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 0 1 1 0 -1 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 0 1 2]
[ 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 0 0 -1 0 0 1 0 0 0 2 1 0 1 1 0 0 1 1 1 0 1 0 1]
[ 0 1 1 0 0 1 0 1 1 1 1 0 1 1 0 0 1 0 2 0 0 0 -1 1 0 0 0 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1]
[ 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 2 0 1 0 0 0 0 1 -1 1 0 0 1 1 1 0 1 0 1 0 1 0 0 1 0 1 1]
[ 0 0 1 1 0 1 1 2 0 0 1 0 0 0 1 0 0 0 1 1 0 1 0 1 -1 1 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 1]
[ 0 1 0 0 1 1 0 0 1 1 1 0 2 1 1 1 0 0 1 0 0 0 0 0 1 -1 0 0 1 1 1 1 1 0 0 0 1 0 1 0 1 1]
[ 0 0 0 1 0 0 0 1 0 1 2 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 -1 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1]
[ 1 1 0 0 1 1 0 0 2 1 0 0 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 -1 1 1 1 1 1 0 0 0 1 0 0 1 0 0]
[ 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 2 1 1 0 1 1 1 -1 0 1 0 0 1 1 0 0 0 1 0 1 0]
[ 0 1 1 1 0 0 0 1 0 1 1 1 0 1 0 0 1 0 1 0 1 1 0 1 0 1 0 1 0 -1 1 0 0 1 2 0 0 1 0 1 1 0]
[ 1 0 1 0 0 0 1 0 0 0 0 1 0 1 0 1 1 2 0 0 0 0 1 0 1 1 1 1 1 1 -1 0 0 1 0 1 1 1 1 0 0 1]
[ 0 1 2 0 0 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 1 0 0 0 -1 0 1 1 0 1 1 1 0 1 1]
[ 0 1 1 1 1 0 0 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 0 0 0 -1 2 1 0 0 0 1 0 1 0]
[ 1 0 0 0 0 1 1 1 1 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 1 1 1 1 2 -1 0 1 1 1 0 1 0 1]
[ 1 0 0 0 1 1 1 0 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 0 1 0 1 2 0 1 1 0 -1 1 1 0 1 0 0 1]
[ 0 2 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 0 1 0 0 0 1 0 0 1 1 -1 1 0 1 0 1 0]
[ 0 0 0 2 1 0 0 1 0 1 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 0 1 1 1 -1 0 0 1 1 0]
[ 0 1 0 1 2 1 0 0 1 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 1 0 1 0 0 1 1 1 0 1 0 0 0 -1 1 0 1 0]
[ 1 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 1 0 1 1 0 1 -1 2 0 0]
[ 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 1 0 1 0 0 0 1 1 0 1 0 1 1 0 1 0 0 0 1 0 0 1 0 2 -1 1 1]
[ 2 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 1 0 1 -1 0]
[ 1 1 0 1 1 0 0 0 1 1 0 1 0 0 0 0 1 0 0 1 2 1 1 1 1 1 1 0 0 0 1 1 0 1 1 0 0 0 0 1 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
dP2(3):D15
order := 30,
length := 12096,
subgroup := MatrixGroup(9, Integer Ring) of order 2 * 3 * 5
Generators:
[ 3 1 2 1 0 1 1 0 0]
[-1 0 -1 0 0 -1 0 0 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[-1 0 -1 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[-1 -1 -1 0 0 0 0 0 0]
[-1 0 -1 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 3 3 2 2 2 2 1 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[-1 -1 -1 0 0 0 0 0 0]
[-2 -1 -1 -1 -1 0 -1 0 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[-2 -1 -1 -1 -1 -1 0 0 0]
[-3 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 5 2 0 2 2 2 2 2 0]
[-2 0 0 -1 -1 -1 -1 -1 0]
[-2 -1 0 -1 -1 -1 -1 0 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-2 -1 0 -1 0 -1 -1 -1 0]
[-2 -1 0 -1 -1 0 -1 -1 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{6,10,10,30}
Orbit:
1
{@
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 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 0 0 0 -1 -1 0),
Mod: (0 0 0 0 0 0 1 0 0)
@}
Intersection Matrix:
[-1 1 1 0 0 2]
[ 1 -1 0 1 2 0]
[ 1 0 -1 2 1 0]
[ 0 1 2 -1 0 1]
[ 0 2 1 0 -1 1]
[ 2 0 0 1 1 -1]
Stabilizer Group Name:
C5
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 1 0 0 0 0 1 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 0 -1 0 0 0 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 -1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
2
{@
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 1 -1 0 0 0 -1 0 0 0),
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: ( 1 0 0 -1 0 -1 0 0 0)
@}
Intersection Matrix:
[-1 1 1 0 0 1 0 1 0 2]
[ 1 -1 1 2 0 0 1 1 0 0]
[ 1 1 -1 0 1 0 1 0 2 0]
[ 0 2 0 -1 1 1 0 0 1 1]
[ 0 0 1 1 -1 0 1 2 0 1]
[ 1 0 0 1 0 -1 2 1 1 0]
[ 0 1 1 0 1 2 -1 0 0 1]
[ 1 1 0 0 2 1 0 -1 1 0]
[ 0 0 2 1 0 1 0 1 -1 1]
[ 2 0 0 1 1 0 1 0 1 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[ 5 2 0 2 2 2 2 2 0]
[-2 0 0 -1 -1 -1 -1 -1 0]
[-2 -1 0 -1 -1 -1 -1 0 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-2 -1 0 -1 0 -1 -1 -1 0]
[-2 -1 0 -1 -1 0 -1 -1 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
3
{@
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0)
@}
Intersection Matrix:
[-1 1 1 0 0 2 1 1 0 0]
[ 1 -1 1 1 2 0 0 0 0 1]
[ 1 1 -1 0 0 0 0 1 2 1]
[ 0 1 0 -1 0 1 0 2 1 1]
[ 0 2 0 0 -1 1 1 1 1 0]
[ 2 0 0 1 1 -1 0 0 1 1]
[ 1 0 0 0 1 0 -1 1 1 2]
[ 1 0 1 2 1 0 1 -1 0 0]
[ 0 0 2 1 1 1 1 0 -1 0]
[ 0 1 1 1 0 1 2 0 0 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[ 5 2 0 2 2 2 2 2 0]
[-2 0 0 -1 -1 -1 -1 -1 0]
[-2 -1 0 -1 -1 -1 -1 0 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-2 -1 0 -1 0 -1 -1 -1 0]
[-2 -1 0 -1 -1 0 -1 -1 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
4
{@
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0),
Mod: (0 0 0 1 0 0 0 0 0),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: (0 0 0 0 1 0 0 0 0),
Mod: ( 1 -1 -1 0 0 0 0 0 0),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 3 -1 -1 -2 -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 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 2 0 0 -1 -1 -1 -1 -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: (0 0 0 0 0 1 0 0 0),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: (0 1 0 0 0 0 0 0 0),
Mod: ( 1 0 -1 0 0 0 0 -1 0)
@}
Intersection Matrix:
[-1 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 0 2 0 1]
[ 1 -1 0 1 1 0 0 0 1 1 2 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 0 0 0]
[ 0 0 -1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 2 0 0 1 0 0]
[ 0 1 1 -1 0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 0 1 0 1 0 0 1 1 1 2]
[ 1 1 1 0 -1 1 1 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 0 0 0 2 1]
[ 0 0 0 0 1 -1 0 0 1 2 1 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 1 1 0 1]
[ 1 0 0 1 1 0 -1 0 2 1 1 0 0 1 1 0 0 1 1 1 0 0 1 0 1 1 1 0 0 0]
[ 1 0 0 1 0 0 0 -1 1 1 1 0 1 0 0 0 1 1 2 1 1 1 0 0 1 1 0 0 1 0]
[ 0 1 1 0 0 1 2 1 -1 0 0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 1]
[ 1 1 1 1 0 2 1 1 0 -1 0 1 0 1 1 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0]
[ 0 2 1 0 0 1 1 1 0 0 -1 0 1 1 1 0 0 1 0 1 1 0 0 1 0 0 0 1 1 1]
[ 0 1 0 1 1 0 0 0 1 1 0 -1 1 1 0 0 1 2 1 1 1 0 0 0 1 1 0 1 0 0]
[ 1 0 0 1 1 1 0 1 1 0 1 1 -1 1 1 1 0 0 0 0 0 0 2 1 1 0 1 0 0 0]
[ 0 0 0 0 0 0 1 0 0 1 1 1 1 -1 0 0 1 0 1 1 1 2 0 1 1 0 0 1 1 1]
[ 0 0 0 1 1 0 1 0 0 1 1 0 1 0 -1 1 2 1 1 0 1 1 0 0 1 1 0 1 0 0]
[ 0 1 0 0 0 0 0 0 1 1 0 0 1 0 1 -1 0 1 1 2 1 1 0 1 1 0 0 1 1 1]
[ 1 1 1 0 0 1 0 1 1 0 0 1 0 1 2 0 -1 0 0 1 0 0 1 1 0 0 1 0 1 1]
[ 1 0 1 0 0 1 1 1 0 0 1 2 0 0 1 1 0 -1 0 0 0 1 1 1 0 0 1 0 1 1]
[ 0 1 1 0 1 1 1 2 0 0 0 1 0 1 1 1 0 0 -1 0 0 0 1 1 0 0 1 1 0 1]
[ 1 0 1 1 1 1 1 1 0 0 1 1 0 1 0 2 1 0 0 -1 0 0 1 0 0 1 1 0 0 0]
[ 1 0 1 0 1 0 0 1 1 1 1 1 0 1 1 1 0 0 0 0 -1 0 1 0 0 1 2 0 0 1]
[ 1 1 1 1 1 1 0 1 1 0 0 0 0 2 1 1 0 1 0 0 0 -1 1 0 0 1 1 0 0 0]
[ 0 1 1 0 0 0 1 0 0 1 0 0 2 0 0 0 1 1 1 1 1 1 -1 0 0 1 0 1 1 1]
[ 1 0 1 1 1 0 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 0 -1 0 2 1 0 0 0]
[ 1 1 2 0 0 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 -1 1 1 0 1 1]
[ 0 1 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 1 1 2 1 -1 0 1 1 1]
[ 0 1 0 1 0 1 1 0 0 0 0 0 1 0 0 0 1 1 1 1 2 1 0 1 1 0 -1 1 1 0]
[ 2 0 1 1 0 1 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 0 0 1 1 -1 1 0]
[ 0 0 0 1 2 0 0 1 1 1 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 1 1 1 -1 0]
[ 1 0 0 2 1 1 0 0 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
dP2(4): C3⋊F5
order := 60,
length := 12096,
subgroup := MatrixGroup(9, Integer Ring) of order 2^2 * 3 * 5
Generators:
[ 4 2 2 1 1 0 1 2 0]
[-1 -1 -1 0 0 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-2 -1 -1 -1 0 0 -1 -1 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 -1 -1 -1 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 6 3 1 2 2 2 2 3 0]
[-3 -1 -1 -1 -1 -1 -1 -2 0]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-2 -1 0 -1 0 -1 -1 -1 0]
[-2 -1 0 -1 -1 0 -1 -1 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[-3 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 6 2 3 2 1 2 2 3 0]
[-3 -1 -1 -1 -1 -1 -1 -2 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-2 -1 -1 -1 0 -1 0 -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]
[ 2 0 1 0 1 0 1 0 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 0 -1 0 0 0 -1 0 0]
[-1 0 -1 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:{6,10,10,30}
Orbit:
1
{@
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 1 0 0 0 0 -1 0 -1 0),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0)
@}
Intersection Matrix:
[-1 1 0 0 2 1]
[ 1 -1 1 2 0 0]
[ 0 1 -1 0 1 2]
[ 0 2 0 -1 1 1]
[ 2 0 1 1 -1 0]
[ 1 0 2 1 0 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[ 6 3 1 2 2 2 2 3 0]
[-3 -1 -1 -1 -1 -1 -1 -2 0]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-2 -1 0 -1 0 -1 -1 -1 0]
[-2 -1 0 -1 -1 0 -1 -1 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[-3 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 5 2 2 2 2 2 0 2 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[-2 -1 -1 -1 -1 0 0 -1 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: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 1 0 -1 -1 0 0 0 0 0),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: (0 1 0 0 0 0 0 0 0),
Mod: ( 1 -1 -1 0 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 1 0 1 1 1 1 0 1]
[ 0 -1 1 1 0 0 1 1 1 1]
[ 1 1 -1 1 1 0 1 1 0 0]
[ 0 1 1 -1 1 1 0 1 1 0]
[ 1 0 1 1 -1 1 1 0 1 0]
[ 1 0 0 1 1 -1 0 1 1 1]
[ 1 1 1 0 1 0 -1 0 1 1]
[ 1 1 1 1 0 1 0 -1 0 1]
[ 0 1 0 1 1 1 1 0 -1 1]
[ 1 1 0 0 0 1 1 1 1 -1]
Stabilizer Group Name:
C6
MatrixGroup(9, Integer Ring)
Generators:
[ 2 0 1 0 1 0 1 0 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 0 -1 0 0 0 -1 0 0]
[-1 0 -1 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 2 3 2 2 3 1 2 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-3 -1 -1 -1 -1 -2 -1 -1 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[-1 0 -1 0 0 -1 0 0 0]
[-2 -1 -1 -1 -1 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
3
{@
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: ( 3 -2 -1 -1 -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: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: (0 0 0 1 0 0 0 0 0),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0)
@}
Intersection Matrix:
[-1 1 1 1 1 0 1 0 1 0]
[ 1 -1 1 0 1 1 1 1 0 0]
[ 1 1 -1 1 0 0 1 1 0 1]
[ 1 0 1 -1 1 0 0 1 1 1]
[ 1 1 0 1 -1 1 0 1 1 0]
[ 0 1 0 0 1 -1 1 1 1 1]
[ 1 1 1 0 0 1 -1 0 1 1]
[ 0 1 1 1 1 1 0 -1 0 1]
[ 1 0 0 1 1 1 1 0 -1 1]
[ 0 0 1 1 0 1 1 1 1 -1]
Stabilizer Group Name:
C6
MatrixGroup(9, Integer Ring)
Generators:
[ 2 0 1 0 1 0 1 0 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 0 -1 0 0 0 -1 0 0]
[-1 0 -1 0 -1 0 0 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 -1 0 0 0 -1 0 0 0),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: (0 0 0 0 1 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 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 1 0 0 -1 -1 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 -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: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0),
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: ( 1 0 0 -1 0 -1 0 0 0),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: (0 0 0 0 0 0 1 0 0)
@}
Intersection Matrix:
[-1 1 0 0 1 1 1 1 0 0 0 1 1 1 0 1 0 0 0 0 2 1 1 1 0 1 0 0 1 0]
[ 1 -1 0 1 0 0 1 0 1 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 0 0 2 0 1 1]
[ 0 0 -1 0 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 1 2 1 0 0 1 0 1 0]
[ 0 1 0 -1 1 2 1 1 1 1 1 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0]
[ 1 0 1 1 -1 0 1 0 0 1 0 0 1 0 1 0 1 0 2 0 0 1 0 0 1 1 1 1 0 1]
[ 1 0 1 2 0 -1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 1 0 1 0 0 1 1 0 1]
[ 1 1 1 1 1 0 -1 0 0 0 1 0 1 1 1 1 1 2 0 1 0 0 0 0 1 0 0 1 0 0]
[ 1 0 1 1 0 0 0 -1 0 0 1 0 1 1 1 1 2 1 1 0 0 0 0 0 1 1 1 0 1 0]
[ 0 1 1 1 0 0 0 0 -1 0 0 0 2 1 1 1 1 1 1 0 1 1 0 0 1 1 0 1 0 0]
[ 0 1 1 1 1 0 0 0 0 -1 1 1 1 1 0 2 1 1 0 0 1 0 0 1 0 1 0 0 1 0]
[ 0 0 0 1 0 0 1 1 0 1 -1 0 1 0 1 0 0 0 1 1 1 2 1 1 0 0 1 1 0 1]
[ 1 0 0 1 0 0 0 0 0 1 0 -1 1 1 2 0 1 1 1 1 0 1 1 0 1 0 1 1 0 0]
[ 1 0 0 0 1 1 1 1 2 1 1 1 -1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1]
[ 1 0 1 1 0 0 1 1 1 1 0 1 0 -1 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 2]
[ 0 1 1 0 1 1 1 1 1 0 1 2 0 0 -1 1 0 0 0 0 1 0 0 1 0 1 0 0 1 1]
[ 1 0 0 0 0 1 1 1 1 2 0 0 0 0 1 -1 0 0 1 1 0 1 1 0 1 0 1 1 0 1]
[ 0 1 0 0 1 1 1 2 1 1 0 1 0 0 0 0 -1 0 0 1 1 1 1 1 0 0 0 1 0 1]
[ 0 0 0 0 0 1 2 1 1 1 0 1 0 0 0 0 0 -1 1 0 1 1 1 1 0 1 1 0 1 1]
[ 0 1 0 0 2 1 0 1 1 0 1 1 0 1 0 1 0 1 -1 1 1 0 1 1 0 0 0 0 1 0]
[ 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0 1 -1 1 0 0 0 1 2 0 0 1 0]
[ 2 0 1 1 0 0 0 0 1 1 1 0 0 0 1 0 1 1 1 1 -1 0 0 0 1 0 1 1 0 1]
[ 1 1 1 0 1 1 0 0 1 0 2 1 0 1 0 1 1 1 0 0 0 -1 0 0 1 1 0 0 1 0]
[ 1 1 2 1 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 0 -1 0 1 1 0 1 0 1]
[ 1 1 1 0 0 1 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 0 0 -1 2 1 0 1 0 0]
[ 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 1 1 1 1 2 -1 0 1 0 1 1]
[ 1 0 0 1 1 0 0 1 1 1 0 0 0 0 1 0 0 1 0 2 0 1 1 1 0 -1 1 1 0 1]
[ 0 2 1 0 1 1 0 1 0 0 1 1 1 1 0 1 0 1 0 0 1 0 0 0 1 1 -1 1 0 0]
[ 0 0 0 0 1 1 1 0 1 0 1 1 0 1 0 1 1 0 0 0 1 0 1 1 0 1 1 -1 2 0]
[ 1 1 1 1 0 0 0 1 0 1 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 0 0 2 -1 1]
[ 0 1 0 0 1 1 0 0 0 0 1 0 1 2 1 1 1 1 0 0 1 0 1 0 1 1 0 0 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 6 3 1 2 2 2 2 3 0]
[-3 -1 -1 -1 -1 -1 -1 -2 0]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-2 -1 0 -1 0 -1 -1 -1 0]
[-2 -1 0 -1 -1 0 -1 -1 0]
[-2 -1 0 -1 -1 -1 0 -1 0]
[-3 -2 -1 -1 -1 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]