//Group G is generated by
//c1c2c3c4c5c6c7c8(1 5)(3 7)(4 6)
//c2c3(1 5 6 3 2 7 4)


3.D7
MatrixGroup(11, Integer Ring) of order 2 * 7
Generators:

    c1c2c3c4c5c6c7c8(1 5)(3 7)(4 6)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 4  1  1  1  1  1  1  1  1  1  0]
    [-1  0  0  0  0  0 -1  0  0  0  0]
    [-1  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  0 -1  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 -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  1]

    c2c3(1 5 6 3 2 7 4)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  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 -1  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  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  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]
1
{@
    Mod: ( 0  1 -1  0  0  0  0  0  0  0  0),
    Mod: (0 0 0 0 0 0 0 0 1 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 0 0 0 1 0 0 0 0 0 0),
    Mod: (0 0 0 1 0 0 0 0 0 0 0),
    Mod: ( 0  1  0  0  0  0  0  0 -1  0  0),
    Mod: (0 0 0 0 0 0 0 1 0 0 0),
    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  1  0 -1  0  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),
    Mod: ( 0  1  0  0  0  0  0 -1  0  0  0)
@}
Intersection Matrix:
[-1  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 -1  0  0  0  0  0  0  1  0  0  0  0]
[ 0  0  0 -1  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  0  0  0  0 -1  0  0  0  0  1  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  0  0  1]
[ 1  0  0  0  0  0  0  0 -1  0  0  0  0  0]c2c8(1 3 8 2 4)(5 6 7)
[ 0  0  1  0  0  0  0  0  0 -1  0  0  0  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  1  0]
[ 0  0  0  0  0  0  0  0  0  0  0  1 -1  0]
[ 0  0  0  0  0  0  0  1  0  0  0  0  0 -1]
Stabilizer Group Name:
C1
MatrixGroup(11, Integer Ring) of order 1
2
{@
    Mod: (0 0 0 0 0 0 0 0 0 1 0),
    Mod: ( 0  1  0  0  0  0  0  0  0 -1  0)
@}
Intersection Matrix:
[-1  1]
[ 1 -1]
Stabilizer Group Name:
C7
MatrixGroup(11, Integer Ring)
Generators:
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  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 -1  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  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  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]