//Group G is generated by //c1c4c6c9(4 6)(7 8) //c1c2c3c4c5c6c7c8(2 3)(4 6)(7 9 8) //c7c9(1 4 6)(7 8 9) //c3c5(2 3 5) //c7c8(7 9 8) 7.C3^3:C2^2 MatrixGroup(11, Integer Ring) of order 2^2 * 3^3 Generators: c1c4c6c9(4 6)(7 8) [ 1 0 0 0 0 0 0 0 0 0 0] [ 2 1 1 0 0 1 0 1 0 0 1] [-1 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 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 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] c1c2c3c4c5c6c7c8(2 3)(4 6)(7 9 8) [ 1 0 0 0 0 0 0 0 0 0 0] [ 4 1 1 1 1 1 1 1 1 0 1] [-1 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] [-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 0 0 -1] [-1 0 0 0 0 0 0 0 -1 0 0] [ 0 0 0 0 0 0 0 0 0 1 0] c7c9(1 4 6)(7 8 9) [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 0 0 0 0 0 1 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 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 1 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] [-1 0 0 0 0 0 0 0 -1 0 0] c3c5(2 3 5) [ 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] [ 0 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 1 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 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] c7c8(7 9 8) [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 0 0 0 0 0 1 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] [ 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 0 -1] [-1 0 0 0 0 0 0 0 -1 0 0] [ 0 0 0 0 0 0 0 0 0 1 0] 1 {@ Mod: ( 0 1 0 0 0 0 0 -1 0 0 0), Mod: ( 0 1 -1 0 0 0 0 0 0 0 0), Mod: (0 0 1 0 0 0 0 0 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 1 0 0 0 0 0) @} Intersection Matrix: [-1 0 0 1 0 0] [ 0 -1 1 0 0 0] [ 0 1 -1 0 0 0] [ 1 0 0 -1 0 0] [ 0 0 0 0 -1 1] [ 0 0 0 0 1 -1] Stabilizer Group Name: C3:S3 MatrixGroup(11, Integer Ring) Generators: [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 0 0 0 0 0 1 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] [ 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 0 -1] [-1 0 0 0 0 0 0 0 -1 0 0] [ 0 0 0 0 0 0 0 0 0 1 0] [ 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] [ 0 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 1 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 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] [ 3 1 0 1 1 0 1 0 1 1 1] [ 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 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 0 0 0 0 0 -1 0 0] [-1 0 0 0 0 0 0 0 0 0 -1] [-1 0 0 0 0 0 0 0 0 -1 0] 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 -1 0 0), Mod: (0 0 0 0 0 0 0 0 1 0 0), Mod: ( 0 1 0 0 0 0 0 0 0 -1 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: C3:S3 MatrixGroup(11, Integer Ring) Generators: [ 1 0 0 0 0 0 0 0 0 0 0] [ 3 1 1 1 1 1 1 1 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 -1 0 0 0 0 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 -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 1 0 0 0 0 0 0 0 0] [ 0 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 1 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 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 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 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] 3 {@ Mod: (0 0 0 1 0 0 0 0 0 0 0), Mod: ( 0 1 0 0 0 0 -1 0 0 0 0), Mod: (0 0 0 0 1 0 0 0 0 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 1 0 -1 0 0 0 0 0 0 0) @} Intersection Matrix: [-1 0 0 0 0 1] [ 0 -1 0 1 0 0] [ 0 0 -1 0 1 0] [ 0 1 0 -1 0 0] [ 0 0 1 0 -1 0] [ 1 0 0 0 0 -1] Stabilizer Group Name: C3:S3 MatrixGroup(11, Integer Ring) Generators: [ 1 0 0 0 0 0 0 0 0 0 0] [ 2 1 1 0 0 1 0 1 0 0 1] [-1 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 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 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] [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 0 0 0 0 0 1 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] [ 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 0 -1] [-1 0 0 0 0 0 0 0 -1 0 0] [ 0 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 1 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 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 1 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] [-1 0 0 0 0 0 0 0 -1 0 0]