//Group G is generated by
//c1c4c5c6c7c8(1 6)(2 3)(4 7)
//c2c3(1 8 6 7 4)(2 5 3)
//c2c5(2 3 5)


2.D15
MatrixGroup(11, Integer Ring)
Generators:
    
    c1c4c5c6c7c8(1 6)(2 3)(4 7)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 3  1  1  0  0  1  1  1  1  1  0]
    [-1  0  0  0  0  0  0 -1  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]
    [-1  0  0  0  0  0  0  0 -1  0  0]
    [-1  0  0  0  0  0 -1  0  0  0  0]
    [-1  0 -1  0  0  0  0  0  0  0  0]
    [-1  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  1]

    c2c3(1 8 6 7 4)(2 5 3)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  0  0  1  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [-1  0  0  0  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  1  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  0  1  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]

    c2c5(2 3 5)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  1  0  0  0  0  0  0]
    [ 0  0  1  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  1  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [-1  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]
1
{@
    Mod: (0 0 1 0 0 0 0 0 0 0 0),
    Mod: (0 0 0 0 0 0 0 1 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 0 0 0 0 1 0),
    Mod: (0 0 0 0 0 1 0 0 0 0 0),
    Mod: (0 0 0 0 0 0 0 0 1 0 0),
    Mod: ( 0  1  0  0  0  0  0  0  0 -1  0),
    Mod: ( 0  1  0  0  0  0  0  0 -1  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  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  0  1  0  0]
[ 0  0  1  0  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:
C3
MatrixGroup(11, Integer Ring)
Generators:
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  1  0  0  0  0  0  0]
    [ 0  0  1  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  1  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [-1  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]
2
{@
    Mod: (0 0 0 1 0 0 0 0 0 0 0),
    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 -1  0  0  0  0  0  0  0)
@}
Intersection Matrix:
[-1  0  0  0  0  1]
[ 0 -1  0  1  0  0]
[ 0  0 -1  0  1  0]
[ 0  1  0 -1  0  0]
[ 0  0  1  0 -1  0]
[ 1  0  0  0  0 -1]
Stabilizer Group Name:
C5
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 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 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 0 0 0]
    [0 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 0 0 0 0 0 0 1]