//Group G is generated by
//c1c5(1 2)(3 4)
//c3c4
//c1c2


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

    c1c5(1 2)(3 4)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  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  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 -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]

    c3c4
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  0  0  1  1  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 -1  0  0  0  0  0]
    [-1  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  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]
    
    c1c2
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  1  1  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  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]
1
{@
    Mod: ( 0  1  0  0  0  0 -1  0  0  0  0),
    Mod: (0 0 0 0 1 0 0 0 0 0 0),
    Mod: (0 0 0 0 0 0 1 0 0 0 0),
    Mod: ( 0  1  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 1 0 0 0 0 0)
@}
Intersection Matrix:
[-1  0  1  0  0  0]
[ 0 -1  0  1  0  0]
[ 1  0 -1  0  0  0]
[ 0  1  0 -1  0  0]
[ 0  0  0  0 -1  1]
[ 0  0  0  0  1 -1]
Stabilizer Group Name:
C2
MatrixGroup(11, Integer Ring)
Generators:
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  1  1  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  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]
2
{@
    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 1 0 0 0 0 0 0 0 0),
    Mod: ( 0  1  0 -1  0  0  0  0  0  0  0)
@}
Intersection Matrix:
[-1  0  0  1]
[ 0 -1  1  0]
[ 0  1 -1  0]
[ 1  0  0 -1]
Stabilizer Group Name:
C3
MatrixGroup(11, Integer Ring)
Generators:
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  0  0  1  1  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 -1  0  0  0  0  0]
    [-1  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  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]