//Group G is generated by
//c2c3c6c7c8c9(1 6 2 5)(3 4)(7 8)
//c1c2c3c4(1 2)(5 6)
//c4c5(4 5 6)(7 9 8)
//c1c3(1 3 2)
//(7 9 8)


8.C3^2:(C3:C4)
MatrixGroup(11, Integer Ring) of order 2^2 * 3^3
Generators:

    c2c3c6c7c8c9(1 6 2 5)(3 4)(7 8)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 3  1  0  1  0  1  1  0  1  1  1]
    [ 0  0  0  0  0  0  0  1  0  0  0]
    [-1  0  0  0  0  0 -1  0  0  0  0]
    [-1  0  0  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  0  0  0  0  0]
    [-1  0  0 -1  0  0  0  0  0  0  0]
    [-1  0  0  0  0  0  0  0  0 -1  0]
    [-1  0  0  0  0  0  0  0 -1  0  0]
    [-1  0  0  0  0  0  0  0  0  0 -1]

    c1c2c3c4(1 2)(5 6)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 2  1  1  1  1  1  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]
    [-1  0  0  0 -1  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  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  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]

    c4c5(4 5 6)(7 9 8)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  0  0  0  1  1  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  0  0  1  0  0  0  0  0  0]
    [-1  0  0  0  0  0 -1  0  0  0  0]
    [-1  0  0  0  0  0  0 -1  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]
    [ 0  0  0  0  0  0  0  0  1  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]

    c1c3(1 3 2)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  1  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 -1  0  0  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  0  0  1  0  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  0  0  1]
    
    (7 9 8)
    [1 0 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 0 0 1 0 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 0 0 1 0 0 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 0 0 1 0 0]
    [0 0 0 0 0 0 0 0 0 1 0]
1
{@
    Mod: (0 0 1 0 0 0 0 0 0 0 0),
    Mod: ( 0  1  0  0  0  0 -1  0  0  0  0),
    Mod: (0 0 0 0 0 0 0 1 0 0 0),
    Mod: ( 0  1  0  0 -1  0  0  0  0  0  0),
    Mod: (0 0 0 0 1 0 0 0 0 0 0),
    Mod: ( 0  1  0  0  0 -1  0  0  0  0  0),
    Mod: ( 0  1  0  0  0  0  0 -1  0  0  0),
    Mod: (0 0 0 0 0 1 0 0 0 0 0),
    Mod: ( 0  1  0 -1  0  0  0  0  0  0  0),
    Mod: (0 0 0 1 0 0 0 0 0 0 0),
    Mod: ( 0  1 -1  0  0  0  0  0  0  0  0),
    Mod: (0 0 0 0 0 0 1 0 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  0  0  1]
[ 0  0 -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  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  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]
[ 1  0  0  0  0  0  0  0  0  0 -1  0]
[ 0  1  0  0  0  0  0  0  0  0  0 -1]
Stabilizer Group Name:
C3^2
MatrixGroup(11, Integer Ring)
Generators:
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  0  0  0  1  1  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  0  0  1  0  0  0  0  0  0]
    [-1  0  0  0  0  0 -1  0  0  0  0]
    [-1  0  0  0  0  0  0 -1  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]
    [ 0  0  0  0  0  0  0  0  1  0  0]
    [ 0  0  0  0  0  0  0  0  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]
    [0 0 1 0 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 0 0 1 0 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 0 0 0 0 1]
    [0 0 0 0 0 0 0 0 1 0 0]
    [0 0 0 0 0 0 0 0 0 1 0]
2
{@
    Mod: (0 0 0 0 0 0 0 0 0 0 1),
    Mod: ( 0  1  0  0  0  0  0  0  0  0 -1),
    Mod: (0 0 0 0 0 0 0 0 0 1 0),
    Mod: (0 0 0 0 0 0 0 0 1 0 0),
    Mod: ( 0  1  0  0  0  0  0  0 -1  0  0),
    Mod: ( 0  1  0  0  0  0  0  0  0 -1  0)
@}
Intersection Matrix:
[-1  1  0  0  0  0]
[ 1 -1  0  0  0  0]
[ 0  0 -1  0  0  1]
[ 0  0  0 -1  1  0]
[ 0  0  0  1 -1  0]
[ 0  0  1  0  0 -1]
Stabilizer Group Name:
C3:S3
MatrixGroup(11, Integer Ring)
Generators:
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 2  1  1  1  1  1  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]
    [-1  0  0  0 -1  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  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  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]

    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 2  1  1  0  1  1  1  0  0  0  0]
    [ 0  0  0  1  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  0  0  0  1  0  0  0]
    [-1  0  0  0  0 -1  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  0]
    [ 0  0  0  0  0  0  0  0  0  1  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  1  1  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 -1  0  0  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  0  0  1  0  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  0  0  1]