//Group G is generated by //c2c7(1 5 4)(2 3 7) //c1c3c5c6c7c9(1 3)(2 4)(5 7)(8 9) //c2c6(1 4 6 2 3 5 7) //(8 9) //c8c9 10.C2^2:F7 MatrixGroup(11, Integer Ring) of order 2^3 * 3 * 7 Generators: c2c7(1 5 4)(2 3 7) [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 1 1 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] [ 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 1 0 0 0 0 0] [ 0 0 0 0 0 0 0 1 0 0 0] [-1 0 0 -1 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] c1c3c5c6c7c9(1 3)(2 4)(5 7)(8 9) [ 1 0 0 0 0 0 0 0 0 0 0] [ 3 1 1 0 1 0 1 1 1 1 0] [-1 0 0 0 -1 0 0 0 0 0 0] [ 0 0 0 0 0 1 0 0 0 0 0] [-1 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 -1 0 0] [-1 0 0 0 0 0 0 -1 0 0 0] [-1 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 -1 0] c2c6(1 4 6 2 3 5 7) [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 1 1 0 0 0 0 0 0] [ 0 0 0 0 0 1 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 0 0 1 0 0 0] [ 0 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 0 0 1 0] [ 0 0 0 0 0 0 0 0 0 0 1] (8 9) [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 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] c8c9 [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 0 0 0 0 0 0 1 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] [-1 0 0 0 0 0 0 0 0 -1 0] [-1 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] [ 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: C2*C6 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 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 0 1] [0 0 0 0 0 0 0 0 0 1 0] [ 1 0 0 0 0 0 0 0 0 0 0] [ 2 1 0 1 0 0 0 0 1 1 1] [ 0 0 1 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 0 0 0] [ 0 0 0 0 0 0 0 1 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 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 -1 0] [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 0 0 0 0 0 0 1 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] [-1 0 0 0 0 0 0 0 0 -1 0] [-1 0 0 0 0 0 0 0 0 0 -1] 2 {@ Mod: (0 0 0 0 0 0 0 0 0 0 1), Mod: ( 0 1 0 0 0 0 0 0 0 0 -1), 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 0 0] [ 1 -1 0 0] [ 0 0 -1 1] [ 0 0 1 -1] Stabilizer Group Name: F7 MatrixGroup(11, Integer Ring) Generators: [ 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 -1 0 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 -1 0 0 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] [-1 0 0 0 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 1] [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 1 1 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] [ 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 1 0 0 0 0 0] [ 0 0 0 0 0 0 0 1 0 0 0] [-1 0 0 -1 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 0 1 1 0 0 0 0 0 0] [ 0 0 0 0 0 1 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 0 0 1 0 0 0] [ 0 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 0 0 1 0] [ 0 0 0 0 0 0 0 0 0 0 1]