# Character: X14 # Comment: induce from Borel # Ind: 1 # Ring: C # Sparsity: 96% # Checker result: pass # Conjugacy class representative result: pass local a, A, b, B, c, C, w, W, i, result, delta, idmat; result := rec(); w := E(3); W := E(3)^2; a := E(5)+E(5)^4; A := -1-a; # b5, b5* b := E(7)+E(7)^2+E(7)^4; B := -1-b; # b7, b7** c := E(11)+E(11)^3+E(11)^4+E(11)^5+E(11)^9; C := -1-c; # b11, b11** i := E(4); result.comment := "L231 as 32 x 32 matrices\n"; result.generators := [ [[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5),0,0,0,0,0,0,0, 0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^3,0, 0,0], [0,0,0,0,0,0,0,0,E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^2, 0,0], [0,0,0,0,0,0,0,0,0,E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,0,0,0,0,0,0,E(5)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,E(5),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0], [0,0,0,0,0,0,E(5),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,0,0,E(5)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5),0,0,0,0,0,0,0,0,0, 0], [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^3 ], [0,0,0,0,0,0,0,0,0,0,E(5)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^2,0,0,0,0, 0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5),0,0,0,0,0,0,0,0,0,0,0,0, 0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5),0,0,0,0,0,0,0,0,0,0, 0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^4,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,0,0,0,0,0,0,0,E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^3,0,0, 0,0], [E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^3,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^2,0,0,0,0,0,0,0, 0,0], [0,E(5)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,E(5)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0]] , [[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5),0,0,0,0,0,0, 0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^4,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^3,0, 0,0], [E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^3,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^2,0,0,0,0,0,0, 0,0], [0,0,E(5)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,0,E(5)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^3, 0,0], [0,0,0,0,0,0,0,0,0,E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^2, 0], [0,0,0,0,0,0,0,0,0,0,E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,0,0,0,0,0,0,0,E(5)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,E(5),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0], [0,0,0,0,0,0,0,E(5),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^2,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,0,0,0,E(5)^2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5),0,0,0,0,0,0,0,0, 0], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5) ], [0,0,0,0,0,0,0,0,0,0,0,E(5)^3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^2,0,0,0, 0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5),0,0,0,0,0,0,0,0,0,0,0, 0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^4,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5),0,0,0,0,0,0,0,0,0, 0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,E(5)^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0]]]; return result;