Magma V2.20-3 Sun Mar 20 2016 10:48:32 on Fordhamwinarski [Seed = 3262786769] Type ? for help. Type -D to quit. > load "autcv10c.txt"; Loading "autcv10c.txt" > G:=SmallGroup(24,14); > RunExample(G,5,[2,2,2,6]); Set seed to 0. Character Table of Group G -------------------------- -------------------------------------------- Class | 1 2 3 4 5 6 7 8 9 10 11 12 Size | 1 1 1 1 3 3 3 3 2 2 2 2 Order | 1 2 2 2 2 2 2 2 3 6 6 6 -------------------------------------------- p = 2 1 1 1 1 1 1 1 1 9 9 9 9 p = 3 1 2 3 4 5 6 7 8 1 4 2 3 -------------------------------------------- X.1 + 1 1 1 1 1 1 1 1 1 1 1 1 X.2 + 1 -1 -1 1 1 -1 -1 1 1 1 -1 -1 X.3 + 1 1 -1 -1 1 1 -1 -1 1 -1 1 -1 X.4 + 1 -1 1 -1 1 -1 1 -1 1 -1 -1 1 X.5 + 1 1 -1 -1 -1 -1 1 1 1 -1 1 -1 X.6 + 1 -1 1 -1 -1 1 -1 1 1 -1 -1 1 X.7 + 1 1 1 1 -1 -1 -1 -1 1 1 1 1 X.8 + 1 -1 -1 1 -1 1 1 -1 1 1 -1 -1 X.9 + 2 2 2 2 0 0 0 0 -1 -1 -1 -1 X.10 + 2 -2 2 -2 0 0 0 0 -1 1 1 -1 X.11 + 2 -2 -2 2 0 0 0 0 -1 -1 1 1 X.12 + 2 2 -2 -2 0 0 0 0 -1 1 -1 1 Conjugacy Classes of group G ---------------------------- [1] Order 1 Length 1 Rep Id(G) [2] Order 2 Length 1 Rep G.2 * G.3 [3] Order 2 Length 1 Rep G.2 [4] Order 2 Length 1 Rep G.3 [5] Order 2 Length 3 Rep G.1 * G.2 * G.3 [6] Order 2 Length 3 Rep G.1 [7] Order 2 Length 3 Rep G.1 * G.3 [8] Order 2 Length 3 Rep G.1 * G.2 [9] Order 3 Length 2 Rep G.4 [10] Order 6 Length 2 Rep G.3 * G.4 [11] Order 6 Length 2 Rep G.2 * G.3 * G.4 [12] Order 6 Length 2 Rep G.2 * G.4 Surface kernel generators: [ G.1 * G.4, G.1 * G.3 * G.4^2, G.2, G.2 * G.3 * G.4^2 ] Is hyperelliptic? true Curve is hyperelliptic > FP,f:=FPGroup(G); > PermG,g:=PermutationGroup(FP); > g(Inverse(f)(G.1 * G.4)); (1, 4)(2, 6)(3, 7)(5, 9) > g(Inverse(f)(G.1 * G.3 * G.4^2)); (1, 11)(2, 12)(3, 8)(4, 7)(5, 10)(6, 9) > g(Inverse(f)(G.2)); (1, 2)(3, 5)(4, 6)(7, 9)(8, 10)(11, 12)