//Group G is generated by //c2c4(1 6)(2 4)(3 5) //c2c5(1 4 3)(2 6 5) //c1c3c5c6(1 5)(3 6) //c3c6(2 4)(3 6) 10.S4 MatrixGroup(11, Integer Ring) of order 2^3 * 3 Generators: c2c4(1 6)(2 4)(3 5) [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 1 0 1 0 0 0 0 0] [ 0 0 0 0 0 0 0 1 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] [-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] c2c5(1 4 3)(2 6 5) [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 1 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 -1 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 -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 0 0 0 0 0 0 0 0 1 0] [ 0 0 0 0 0 0 0 0 0 0 1] c1c3c5c6(1 5)(3 6) [ 1 0 0 0 0 0 0 0 0 0 0] [ 2 1 1 0 1 0 1 1 0 0 0] [-1 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 -1 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] [-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 0 0 1 0] [ 0 0 0 0 0 0 0 0 0 0 1] c3c6(2 4)(3 6) [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 0 1 0 0 1 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] [-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 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 0 0 0 0 0 0 0 1 0] [ 0 0 0 0 0 0 0 0 0 0 1] 1 {@ (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 -1 0 0 0 0), ( 0 1 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 -1 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 1 0 -1 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 1 -1 0 0 0 0 0 0 0 0) @} Intersection Matrix: [-1 0 0 0 0 0 0 0 0 0 0 1] [ 0 -1 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 -1 1 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 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 -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 1 -1 0 0] [ 0 0 1 0 0 0 0 0 0 0 -1 0] [ 1 0 0 0 0 0 0 0 0 0 0 -1] Stabilizer Group Name: C2 MatrixGroup(11, Integer Ring) Generators: [ 1 0 0 0 0 0 0 0 0 0 0] [ 1 1 0 0 1 0 0 1 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] [-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 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 0 0 0 0 0 0 0 1 0] [ 0 0 0 0 0 0 0 0 0 0 1]