# Character: X12 # Comment: induce from Borel, reseed # Ind: 1 # Ring: Z # Sparsity: 67% # Maximum absolute entry: 8 # 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 := [ [[0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [1,0,0,0,0,0,0,1,-1,1,1,0,0,0,0,0,1,0,1,0,0,0,0,0,-1,1,0,0,0,0,0,0 ], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,1,0,-1,-1,-1,0,-1,0,1,0,0,0,0,0,1,0,1,1,0,1,0,0,0,0,0,0,-1,0, 0,0], [1,0,0,1,0,0,1,0,-1,0,0,0,-1,0,0,0,0,0,0,0,-1,0,-1,1,0,0,0,0,0,0,0, 0], [0,-1,-1,1,1,0,0,0,0,0,-1,1,-1,1,0,-1,0,0,-1,-1,-1,0,-1,0,0,0,0,-1, 0,1,0,0], [0,0,-1,-2,1,0,0,2,0,1,0,1,0,0,0,0,1,1,0,0,0,-1,1,-1,0,1,0,0,0,0,1, 0], [0,0,0,2,0,1,1,-1,1,-1,-1,0,1,1,-1,1,-1,-1,0,0,0,0,-1,0,-1,-1,1,0, 0,0,-2,0], [0,0,-1,1,1,1,0,0,1,-1,-1,0,1,1,-1,1,-1,0,0,0,0,-1,-1,-1,-1,-1,1,0, 0,1,-1,0], [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], [0,0,1,1,0,-1,0,-1,0,-1,1,0,-1,0,1,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0, 0,0], [0,-1,-1,2,0,0,0,-1,1,-1,0,1,0,1,0,1,0,0,0,0,0,0,-2,-1,-1,-1,1,0,0, 1,-1,0], [0,1,-2,2,2,3,1,1,1,1,-3,0,1,1,-2,1,-1,-1,0,-1,-1,-2,0,-1,-1,-1,1, 0,0,1,-2,-1], [-1,0,-1,3,1,2,0,-1,2,0,-3,0,1,2,-3,1,-2,-2,0,-1,0,-1,0,-1,-1,-2,1, 0,0,1,-3,-1], [-1,0,-2,2,0,0,-1,-1,2,-2,-1,0,2,0,1,3,-1,1,1,1,1,-1,-1,-3,-1,-2,2, 1,1,1,-1,0], [0,0,0,2,1,2,2,-1,1,1,-1,-1,-1,0,-2,-1,-1,-3,-1,-3,0,0,0,2,0,0,-1, 0,1,0,-1,-1], [1,0,-1,2,0,1,1,0,0,0,-1,0,0,1,0,0,0,0,0,0,-1,0,-1,0,-1,0,1,0,0,0, -1,0], [0,0,-1,5,2,2,1,-2,2,-1,-2,0,0,2,-2,1,-2,-2,-1,-2,0,0,-2,0,-1,-2,1, 0,0,1,-3,-1], [0,0,2,-3,-2,-3,-2,1,-1,0,3,0,1,-2,2,1,2,2,2,2,2,1,1,-1,0,1,0,1,0, -1,2,1], [1,1,2,-1,1,1,2,1,-1,1,0,-1,-1,-1,-1,-2,0,-1,-1,-1,0,0,1,2,1,1,-2, 0,0,-1,1,-1]] , [[-1,0,-1,0,1,1,1,0,0,0,-2,0,0,1,-1,-1,-1,0,-1,0,-1,-2,0,0,0,0,0,-1, 0,0,-1,0], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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,-1,0,0,1,-1,1,0,0,0,0,0,0,0,0,1,1,-1,0,1,0,0,0,0,0,0,0,0, 0], [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,1,0,0,-1,0,0,0,0,1,0,-1,0,1,-1,1,0,0,0,0,1,0,1,0,1,-1,-1,0,-1, 1,0], [1,1,0,-4,-1,-2,-1,1,0,2,1,1,1,-2,2,0,2,2,1,2,0,-1,1,-1,1,1,0,0,-1, -1,3,0], [0,-2,1,7,1,2,2,-2,1,-2,-1,-1,-4,3,-1,-3,-2,-4,-3,-5,-1,4,-2,4,0,0, -1,-1,1,1,-2,0], [1,-3,1,5,1,1,3,-2,0,-1,0,-1,-5,3,0,-4,-1,-4,-3,-4,-2,4,-2,5,0,1,-2, -2,1,0,-1,0], [-1,1,0,-1,0,-1,-1,0,1,0,0,0,1,0,0,0,0,1,0,0,1,-1,0,-1,0,0,0,0,0,0, 0,0], [0,0,1,2,1,1,1,0,-1,0,-1,-1,-2,1,-1,-2,-1,-2,-1,-1,-1,1,0,2,0,1,-1, -1,0,0,-1,0], [2,-3,2,8,1,1,3,-2,0,-2,0,-1,-6,3,0,-4,-1,-5,-3,-5,-2,6,-2,6,0,1,-2, -2,1,0,-1,0], [-1,-1,-2,-3,-1,-4,-2,1,1,1,0,2,1,-1,4,0,2,1,0,0,0,-1,0,0,2,1,0,-2, 0,-1,3,2], [0,-1,-1,0,-2,-1,-1,1,0,0,0,1,0,0,2,0,1,1,0,0,0,1,0,0,0,0,1,0,0,0, 1,1], [0,-1,-1,5,3,2,2,-3,2,-2,-3,-1,-2,3,-2,-1,-3,-4,-3,-4,0,1,-2,2,-1, -1,0,-1,1,1,-3,0], [0,0,-2,-2,-3,-2,-2,1,-1,0,1,2,3,-2,2,3,2,2,3,3,1,-1,1,-3,0,-1,2,1, 0,0,1,1], [0,-1,1,1,1,-1,0,-1,1,-1,0,0,-2,1,1,-2,0,-1,-2,-2,0,2,-1,2,1,1,0,-1, 0,0,1,1], [2,-1,6,6,1,3,3,-1,-1,0,2,-3,-8,2,-1,-5,-1,-3,-3,-4,-2,7,-1,6,0,2, -3,0,0,0,0,-1], [1,1,2,2,2,4,2,-2,1,-1,0,-2,-1,0,-3,0,-2,-1,-1,-1,1,1,-1,0,-1,-1,0, 2,0,1,-2,-2], [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]]]; return result;