//Group G is generated by //c2c4(1 4 2 5 3 6) //c1c3c4c7c8c9(1 5 9)(2 4 7)(3 6 8) //c3c4c5c6(1 2)(4 5) //c1c9(2 3)(4 5 6)(7 8) //c1c2(1 2 3)(4 6 5) //c1c2c7c9(1 2 3)(7 8 9) //c1c2(1 2 3) 13.C3^3.S4 MatrixGroup(11, Integer Ring) of order 2^3 * 3^4 Generators: c2c4(1 4 2 5 3 6) [ 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 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] [-1 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 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] c1c3c4c7c8c9(1 5 9)(2 4 7)(3 6 8) [ 1 0 0 0 0 0 0 0 0 0 0] [ 3 1 1 1 1 0 1 1 1 0 0] [-1 0 0 0 0 0 -1 0 0 0 0] [ 0 0 0 0 0 1 0 0 0 0 0] [-1 0 0 0 0 0 0 -1 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 1 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 -1 0 0 0 0 0 0 0 0] c3c4c5c6(1 2)(4 5) [ 1 0 0 0 0 0 0 0 0 0 0] [ 2 1 0 0 1 1 1 1 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] [-1 0 0 0 -1 0 0 0 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 -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] c1c9(2 3)(4 5 6)(7 8) [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 1 0 0 0 0 0 0 0 1] [-1 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 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 1 0 0] [-1 0 0 0 0 0 0 0 0 0 -1] c1c2(1 2 3)(4 6 5) [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 1 1 0 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] [ 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 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 0 0 1 0] [ 0 0 0 0 0 0 0 0 0 0 1] c1c2c7c9(1 2 3)(7 8 9) [ 1 0 0 0 0 0 0 0 0 0 0] [ 2 1 0 1 1 0 0 0 1 1 0] [-1 0 0 -1 0 0 0 0 0 0 0] [-1 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 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] [-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 -1 0 0] c1c2(1 2 3) [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 1 1 0 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] [ 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 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 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 -1), Mod: (0 0 0 0 0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 -1 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 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 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 -1 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 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 -1 1 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 0 0 0 0 0 0 0 -1 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 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 1] [ 0 1 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 -1 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 0 0 0 0 -1 0 1 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 0 1 0 -1 0] [ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 -1] Stabilizer Group Name: S3^2 MatrixGroup(11, Integer Ring) Generators: [ 1 0 0 0 0 0 0 0 0 0 0] [ 2 1 0 0 1 1 1 1 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] [-1 0 0 0 -1 0 0 0 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 -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] [ 1 1 0 1 0 0 1 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] [-1 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 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] [ 1 1 0 1 1 0 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] [ 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 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 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] [-1 0 0 -1 0 0 0 0 0 0 0] [-1 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 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]