//Group G is generated by //c1c4c5c6c7c8(1 2 3 8)(4 6) //c1c3(1 3)(2 8) //c2c3c6c7(1 8 2 3 5)(4 6 7) //c4c9(6 7) //c6c7(6 7 4) 9.S3*F5 MatrixGroup(11, Integer Ring) of order 2^3 * 3 * 5 Generators: c1c4c5c6c7c8(1 2 3 8)(4 6) [ 1 0 0 0 0 0 0 0 0 0 0] [ 3 1 1 1 0 1 1 1 1 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 0 0 0 0 1 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 -1 0 0 0 0 0] [-1 0 0 0 0 0 0 0 -1 0 0] [-1 0 -1 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 1] c1c3(1 3)(2 8) [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 1 0 1 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] [-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 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 0 0] [ 0 0 0 0 0 0 0 0 0 0 1] c2c3c6c7(1 8 2 3 5)(4 6 7) [ 1 0 0 0 0 0 0 0 0 0 0] [ 2 1 0 0 1 1 1 0 1 0 0] [ 0 0 0 0 0 0 0 0 0 1 0] [-1 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 1 0 0 0 0 0 0 0 0] [-1 0 0 0 0 0 0 0 -1 0 0] [-1 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 0 0 1] c4c9(6 7) [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 0 0 1 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] [-1 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 1 0 0 0] [ 0 0 0 0 0 0 0 0 0 1 0] [-1 0 0 0 0 0 0 0 0 0 -1] c6c7(6 7 4) [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 0 0 1 0 0 1 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 0 1 0 0 0 0] [-1 0 0 0 0 0 0 0 -1 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] 1 {@ Mod: ( 0 1 0 0 0 0 0 -1 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 0 0 0 0 0 0 0 1 0 0), Mod: ( 0 1 0 0 0 0 0 0 -1 0 0), Mod: (0 0 0 0 0 1 0 0 0 0 0) @} Intersection Matrix: [-1 1 0 0 0 0] [ 1 -1 0 0 0 0] [ 0 0 -1 0 0 1] [ 0 0 0 -1 1 0] [ 0 0 0 1 -1 0] [ 0 0 1 0 0 -1] Stabilizer Group Name: F5 MatrixGroup(11, Integer Ring) Generators: [ 1 0 0 0 0 0 0 0 0 0 0] [ 2 1 0 1 0 0 1 0 0 1 1] [-1 0 0 0 0 0 0 0 0 -1 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] [ 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 0 0 0 -1 0 0 0 0] [-1 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 1 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] [-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 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 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 1 0 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 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 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 1 0 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 1 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] [-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 1 0 0 0] [ 0 0 0 0 0 0 0 0 1 0 0] [-1 0 0 0 -1 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 1] 2 {@ 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 0 -1 0 0 0 0 0 0), Mod: (0 0 0 0 1 0 0 0 0 0 0), Mod: (0 0 0 0 0 0 0 0 0 1 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), Mod: (0 0 0 0 0 0 1 0 0 0 0) @} Intersection Matrix: [-1 0 0 0 0 0 0 0 1 0] [ 0 -1 0 0 0 0 0 0 0 1] [ 0 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 1 0 0] [ 0 0 0 0 1 0 -1 0 0 0] [ 0 0 0 0 0 1 0 -1 0 0] [ 1 0 0 0 0 0 0 0 -1 0] [ 0 1 0 0 0 0 0 0 0 -1] Stabilizer Group Name: D6 MatrixGroup(11, Integer Ring) Generators: [ 1 0 0 0 0 0 0 0 0 0 0] [ 2 1 0 1 1 1 0 0 1 0 0] [ 0 0 1 0 0 0 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 0 0 0 0 0 1 0 0 0] [ 0 0 0 0 0 0 0 0 0 1 0] [-1 0 0 0 0 0 0 0 -1 0 0] [-1 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] [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 0 0 1 0 0 1 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 0 1 0 0 0 0] [-1 0 0 0 0 0 0 0 -1 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] [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 0 0 1 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] [-1 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 1 0 0 0] [ 0 0 0 0 0 0 0 0 0 1 0] [-1 0 0 0 0 0 0 0 0 0 -1] 3 {@ Mod: (0 0 0 0 0 0 0 0 0 0 1), Mod: ( 0 1 0 0 0 0 0 0 0 0 -1) @} Intersection Matrix: [-1 1] [ 1 -1] Stabilizer Group Name: C3:F5 MatrixGroup(11, Integer Ring) Generators: [ 1 0 0 0 0 0 0 0 0 0 0] [ 3 1 1 1 0 1 1 1 1 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 0 0 0 0 1 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 -1 0 0 0 0 0] [-1 0 0 0 0 0 0 0 -1 0 0] [-1 0 -1 0 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 1 0 1 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] [-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 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 0 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 0 1 1 1 0 1 0 0] [ 0 0 0 1 0 0 0 0 0 0 0] [ 0 0 1 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] [-1 0 0 0 -1 0 0 0 0 0 0] [-1 0 0 0 0 0 0 0 -1 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] [ 1 0 0 0 0 0 0 0 0 0 0] [ 2 1 0 0 1 1 1 0 1 0 0] [ 0 0 0 0 0 0 0 0 0 1 0] [-1 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 1 0 0 0 0 0 0 0 0] [-1 0 0 0 0 0 0 0 -1 0 0] [-1 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 0 0 1] [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 0 0 1 0 0 1 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 0 1 0 0 0 0] [-1 0 0 0 0 0 0 0 -1 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]