//Group G is generated by
//c1c3c5c6c7c8(1 3 4 2)(5 6)
//c2c3(1 4)(2 3)
//c2c8(1 3 8 2 4)(5 6 7)
//(5 7 6)


4.C3:F5
MatrixGroup(11, Integer Ring) of order 2^2 * 3 * 5
Generators:

    c1c3c5c6c7c8(1 3 4 2)(5 6)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 3  1  0  0  1  1  1  1  1  1  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  0 -1  0  0  0  0  0]
    [ 0  0  0  1  0  0  0  0  0  0  0]
    [-1  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  0  0  0 -1  0  0]
    [-1  0  0  0  0  0  0  0  0 -1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]

    c2c3(1 4)(2 3)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  1  0  0  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [-1  0  0  0 -1  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  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]

    c2c8(1 3 8 2 4)(5 6 7)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  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  0  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  0  0  0  1  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]
    [-1  0  0 -1  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]

    (5 7 6)
    [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 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
{@
    Mod: (0 0 1 0 0 0 0 0 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 0 0 0 0 0 0 0 0 1 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  1  0  0  0  0  0  0  0 -1  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)
@}
Intersection Matrix:
[-1  0  0  0  0  0  0  0  0  1]
[ 0 -1  1  0  0  0  0  0  0  0]
[ 0  1 -1  0  0  0  0  0  0  0]
[ 0  0  0 -1  0  1  0  0  0  0]
[ 0  0  0  0 -1  0  0  1  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  1  0  0 -1  0  0]
[ 0  0  0  0  0  0  1  0 -1  0]
[ 1  0  0  0  0  0  0  0  0 -1]
Stabilizer Group Name:
C6
MatrixGroup(11, Integer Ring)
Generators:
    [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 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  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  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  0  0]
    [-1  0  0 -1  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]
2
{@
    Mod: ( 0  1  0  0  0  0  0 -1  0  0  0),
    Mod: ( 0  1  0  0  0  0 -1  0  0  0  0),
    Mod: (0 0 0 0 0 0 1 0 0 0 0),
    Mod: (0 0 0 0 0 0 0 1 0 0 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)
@}
Intersection Matrix:
[-1  0  0  1  0  0]
[ 0 -1  1  0  0  0]
[ 0  1 -1  0  0  0]
[ 1  0  0 -1  0  0]
[ 0  0  0  0 -1  1]
[ 0  0  0  0  1 -1]
Stabilizer Group Name:
D5
MatrixGroup(11, Integer Ring)
Generators:
    [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 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 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 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 0 1]

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