//Group G is generated by //c1c2c3c4(1 4 7 6) //c4c6(1 7)(4 6) //c4c6(1 3 7 4 6) //c2c5 8.C2*F5 MatrixGroup(11, Integer Ring) of order 2^3 * 5 Generators: c1c2c3c4(1 4 7 6) [ 1 0 0 0 0 0 0 0 0 0 0] [ 2 1 0 1 1 1 0 0 1 0 0] [-1 0 0 0 0 -1 0 0 0 0 0] [-1 0 0 -1 0 0 0 0 0 0 0] [-1 0 0 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 1 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 0 0 0 0 1 0] [ 0 0 0 0 0 0 0 0 0 0 1] c4c6(1 7)(4 6) [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 0 0 1 0 1 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] [-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 -1 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 0 0 0 0 1] c4c6(1 3 7 4 6) [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 1 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] [ 0 0 0 0 0 0 0 0 1 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 -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 0 0 0 1 0] [ 0 0 0 0 0 0 0 0 0 0 1] c2c5 [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 1 0 0 1 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 1 0 0 0 0 0 0] [ 0 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 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 {@ (0 0 0 1 0 0 0 0 0 0 0), ( 0 1 0 -1 0 0 0 0 0 0 0) @} Intersection Matrix: [-1 1] [ 1 -1] Stabilizer Group Name: F5 MatrixGroup(11, Integer Ring) Generators: [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 0 0 1 0 1 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] [-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 -1 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 0 0 0 0 1] [ 1 0 0 0 0 0 0 0 0 0 0] [ 3 1 1 0 1 1 1 1 1 0 0] [-1 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 -1 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 0 0 0 0 0 -1 0 0 0] [-1 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 0 0 0 0 1] [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 1 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] [ 0 0 0 0 0 0 0 0 1 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 -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 0 0 0 1 0] [ 0 0 0 0 0 0 0 0 0 0 1] 2 {@ ( 0 1 0 0 0 0 0 -1 0 0 0), ( 0 1 -1 0 0 0 0 0 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), (0 0 1 0 0 0 0 0 0 0 0), (0 0 0 0 0 0 0 1 0 0 0), ( 0 1 0 0 0 -1 0 0 0 0 0), ( 0 1 0 0 0 0 0 0 -1 0 0), (0 0 0 0 0 0 0 0 1 0 0), (0 0 0 0 0 1 0 0 0 0 0) @} Intersection Matrix: [-1 0 0 0 0 1 0 0 0 0] [ 0 -1 0 0 1 0 0 0 0 0] [ 0 0 -1 1 0 0 0 0 0 0] [ 0 0 1 -1 0 0 0 0 0 0] [ 0 1 0 0 -1 0 0 0 0 0] [ 1 0 0 0 0 -1 0 0 0 0] [ 0 0 0 0 0 0 -1 0 0 1] [ 0 0 0 0 0 0 0 -1 1 0] [ 0 0 0 0 0 0 0 1 -1 0] [ 0 0 0 0 0 0 1 0 0 -1] Stabilizer Group Name: C2^2 MatrixGroup(11, Integer Ring) Generators: [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 1 0 0 1 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 1 0 0 0 0 0 0] [ 0 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 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 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 1 0 0 0 0 0 0 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 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 0] [0 0 0 0 0 0 0 0 0 0 1] 3 {@ ( 0 1 0 0 0 0 -1 0 0 0 0), (0 0 0 0 0 0 1 0 0 0 0) @} Intersection Matrix: [-1 1] [ 1 -1] Stabilizer Group Name: F5 MatrixGroup(11, Integer Ring) Generators: [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 0 0 1 0 1 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] [-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 -1 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 0 0 0 0 1] [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 1 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] [ 0 0 0 0 0 0 0 0 1 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 -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 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 0 1 1 1 0 0 1 0 0] [-1 0 0 0 0 -1 0 0 0 0 0] [-1 0 0 -1 0 0 0 0 0 0 0] [-1 0 0 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 1 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 0 0 0 0 1 0] [ 0 0 0 0 0 0 0 0 0 0 1]