H1 programs

Orbit decompositions E7 nonconic


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]