# Character: X12 # Comment: perm rep on 144 pts # Ind: 1 # Ring: Z # Sparsity: 72% # Maximum absolute entry: 12 # Checker result: pass # Conjugacy class representative result: pass local b, B, w, W, i, result, delta, idmat; result := rec(); w := E(3); W := E(3)^2; b := E(7)+E(7)^2+E(7)^4; B := -1-b; # b7, b7** i := E(4); result.comment := "L33 as 39 x 39 matrices\n"; result.generators := [ [[-2,0,1,1,0,-1,-1,0,-1,0,0,0,-1,-1,1,0,0,0,1,1,-1,0,0,0,-1,0,0,1, 0,-1,1,-1,0,0,-1,1,0,0,0], [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], [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,1,0,0,-1,0,1,1,0,0,1,0,1,0,-1,2,2,1,0,1,1,0,0,1,1,-1,-1,1,0,0,0, 0,0,1,0,0,1,0,0], [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], [-2,-1,1,1,0,-1,-2,0,-1,1,-1,0,-1,-2,2,-2,-1,-1,0,1,-1,0,0,-1,-1,0, 1,1,0,-1,1,-1,-1,-1,-1,0,0,0,0], [-1,-1,1,1,1,-1,-2,-1,-1,1,-1,0,-1,-2,2,-3,-2,-1,0,0,-1,0,0,-2,-1, 0,1,0,0,-1,1,0,-1,-1,-1,0,0,0,0], [-3,-1,1,1,0,0,-2,0,-1,0,-1,-1,-1,-2,2,-2,-1,-1,0,1,-1,1,1,-1,-1,0, 1,1,0,-1,1,-1,-1,-1,-2,0,-1,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [-2,-2,2,2,0,-1,-3,0,-2,0,0,0,-2,-2,3,-1,-1,-1,1,1,-1,0,0,-1,-1,0, 1,1,0,-3,1,-1,0,-1,-2,-1,0,0,0], [0,1,-1,-1,1,0,0,-1,1,-1,1,-1,1,1,0,-1,-1,1,0,0,1,0,0,-1,1,0,-1,-1, -1,0,-1,1,1,-1,0,1,0,0,0], [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, 1,0,0,0,0,0,0], [-7,-5,6,6,0,-3,-6,0,-6,1,-1,0,-4,-7,6,-4,-2,-4,2,5,-3,3,1,-2,-3,0, 4,4,0,-5,4,-3,-3,-2,-6,-2,0,0,0], [-1,-3,2,2,1,-1,-4,-1,-3,1,-1,1,-2,-2,4,-4,-3,-2,0,0,-1,1,-1,-2,-1, 1,2,0,0,-3,1,0,-1,-2,-2,-2,0,0,0], [-2,-2,2,2,0,-1,-3,0,-2,0,0,0,-2,-2,3,-1,-1,-1,1,1,-1,0,0,-1,-1,0, 1,1,0,-2,1,-1,0,-1,-2,-1,0,0,0], [4,2,-3,-3,-1,2,4,1,3,0,0,0,2,4,-4,4,3,2,-1,-2,2,-2,-1,3,2,-1,-2,-1, 0,3,-2,1,1,2,3,0,0,0,0], [-2,-2,2,2,-1,0,-2,0,-2,1,-1,0,-1,-2,2,-1,-1,-2,0,1,-1,1,1,-1,-1,0, 2,2,0,-2,1,-1,-2,-1,-2,-2,0,0,0], [0,1,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,0,0,0,0,0, 0,0,0,1,0,0,0], [2,1,-1,-2,1,0,1,-1,2,0,0,0,1,1,-2,0,0,1,-1,-1,1,-1,0,0,0,0,-1,-2, 0,2,-1,1,1,0,2,1,0,0,0], [1,4,-3,-6,0,1,4,-1,3,-2,2,-2,3,3,-4,0,1,4,-1,0,2,-1,1,0,2,0,-4,-1, 0,2,-2,1,0,0,2,6,0,-1,0], [0,0,0,-2,1,1,0,-1,1,-1,1,-1,1,1,0,-1,-1,1,0,0,1,0,0,-1,1,0,-1,-1, 0,0,-1,1,1,-1,0,1,0,0,-1]] , [[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], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [-2,0,1,1,0,-1,-1,0,-1,0,0,0,-1,-1,1,0,0,0,1,1,-1,0,0,0,-1,0,0,1,0, -1,1,-1,0,0,-1,1,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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,-1,1,0,0,0,0,0,0,0,0, 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,-1,0,1,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,1], [-1,1,0,-1,0,-1,1,0,0,-1,0,-1,0,0,0,0,0,1,0,0,0,0,1,-1,0,0,-1,0,0, 0,0,0,0,0,0,2,0,0,0], [-1,1,0,-1,0,-1,1,0,0,-1,1,-1,0,0,0,0,0,1,0,0,0,0,1,-1,0,0,-1,0,0, 0,0,0,0,0,0,2,0,0,0], [-1,1,0,-1,0,-1,1,0,0,-1,0,0,0,0,0,0,0,1,0,0,0,0,1,-1,0,0,-1,0,0,0, 0,0,0,0,0,2,0,0,0], [-1,0,0,0,-1,0,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0,1,0, 0,0,0,0,0,0,0], [1,0,0,0,0,0,1,0,0,1,0,1,0,0,-1,1,1,0,0,-1,0,0,0,0,0,0,0,0,1,1,0,0, 0,1,1,0,0,1,0], [4,2,-2,1,-5,2,5,5,2,3,-1,4,0,2,-7,12,8,1,0,-1,0,-2,-2,8,1,-1,-1,1, 3,4,1,-1,2,6,5,-3,1,2,1], [-1,0,1,0,-1,0,0,1,-1,0,0,0,0,-1,-1,1,1,0,0,1,0,1,0,1,0,0,0,1,1,0, 1,-1,-1,1,0,1,0,0,0], [0,1,0,0,0,-2,0,0,1,0,0,0,1,1,0,0,0,1,0,0,0,-1,0,0,-1,0,0,0,0,0,0, 0,1,1,1,1,0,-1,0], [-2,3,0,-3,1,0,1,-2,2,-3,1,-3,2,1,-1,-3,-1,2,-1,0,2,1,1,-2,2,0,-3, -1,-1,0,-1,1,0,-1,-1,5,-1,-1,0], [2,1,-2,-2,-3,4,4,3,1,1,1,1,1,1,-5,7,5,1,-1,-1,1,0,-1,5,2,0,-2,0,3, 4,0,0,1,3,3,-1,0,2,0], [0,2,0,-1,-1,-1,2,0,1,0,0,0,1,0,-2,1,1,1,-1,0,0,0,1,0,0,0,-1,0,0,1, 0,0,0,1,1,2,0,0,1], [-1,-3,1,1,2,-1,-4,-2,-2,1,0,0,-2,-1,5,-4,-3,-2,1,1,-1,0,1,-3,-2,1, 2,0,-1,-2,0,0,0,-3,-2,-2,0,0,-1], [1,1,-2,0,-2,2,3,2,1,0,-1,1,0,0,-3,4,3,0,0,-1,0,0,-1,3,2,-1,-1,0,1, 2,0,0,0,2,1,-1,0,1,1], [1,0,0,0,-1,1,1,1,0,1,0,1,0,0,-1,2,1,0,0,-1,0,0,0,1,0,0,0,0,1,1,0, 0,0,1,1,-1,0,1,0], [-3,-2,2,1,2,-2,-3,-2,-2,0,0,-1,-1,-2,3,-6,-4,-2,0,0,-1,2,2,-4,-2, 1,1,0,0,-2,1,0,-1,-2,-2,1,-1,0,0], [2,-1,-1,2,-1,2,1,1,0,1,-1,2,-1,0,-1,3,2,-2,0,-2,0,0,-1,2,1,0,1,0, 1,2,0,0,0,1,1,-4,0,2,0], [-6,-4,5,4,0,-2,-5,-1,-5,1,-1,0,-3,-6,5,-4,-2,-3,1,3,-2,3,1,-3,-2, 0,3,3,0,-4,3,-2,-3,-2,-5,-1,0,0,0]]]; return result;