# Character: X11 # Comment: perm rep on 144 pts # Ind: 1 # Ring: Z # Sparsity: 70% # Maximum absolute entry: 6 # 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 27 x 27 matrices\n"; result.generators := [ [[0,0,0,0,1,0,1,0,0,1,0,0,0,0,-1,0,-1,1,0,0,0,0,-1,-1,0,-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], [0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [-1,0,1,-1,0,0,-1,0,0,-1,0,1,0,1,0,0,0,1,0,-1,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,-1,0,0,0,-1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0,1,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,-1,0,1,0,0,0,0,0,0,0,0,0,0], [-1,-1,1,0,1,0,0,0,-2,-1,1,1,-1,1,0,-1,0,1,0,0,0,0,-1,-1,0,1,0], [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], [1,0,0,0,-1,-1,-1,0,1,0,0,0,0,0,1,1,0,-1,1,0,0,0,1,1,0,0,0], [1,2,-2,0,-1,-1,0,0,2,2,-1,-1,1,-1,-1,1,1,-1,0,1,0,0,1,1,0,0,0], [2,4,-6,2,2,-1,3,0,3,5,-1,-4,2,-2,-4,1,1,-1,0,2,1,-2,0,0,-1,-1,0], [1,1,-2,0,1,-1,1,1,2,2,0,-1,0,-1,-2,1,0,0,0,1,0,0,0,0,-1,-1,0], [0,0,1,-2,-2,1,-1,1,0,-1,-1,1,0,-1,2,0,0,-1,0,-1,0,1,2,1,1,1,0], [-1,1,-1,1,1,0,0,-1,0,1,1,-1,1,1,-1,0,-1,1,0,0,0,0,-1,0,0,-1,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0], [-1,-1,1,0,1,0,0,0,-2,-1,1,1,-1,1,0,0,0,1,0,0,0,0,-1,-1,0,0,0], [3,2,-4,1,1,-1,3,1,4,3,-2,-2,0,-3,-4,2,2,-1,0,2,0,-2,1,1,-2,-1,1]] , [[-1,0,1,-1,0,0,-1,0,0,-1,0,1,0,1,0,0,0,1,0,-1,0,1,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,1,0,1,0,0,1,0,0,0,0,-1,0,-1,1,0,0,0,0,-1,-1,0,-1,0], [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], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0], [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,-1,1,0,0,-1,-1,0,-1,-1,1,1,-1,1,1,0,0,0,1,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [-1,-1,1,-1,0,0,0,0,-1,-1,0,0,-1,0,0,-1,1,0,-1,0,0,0,0,0,0,1,0], [1,1,-1,1,0,0,0,-1,1,1,0,-1,1,0,0,1,-1,0,1,1,-1,0,-1,1,0,-1,0], [-1,-1,2,0,-1,-1,-3,-1,0,-1,1,2,0,2,2,0,0,0,1,0,-1,1,0,1,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [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], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [-1,-2,1,-1,0,1,0,2,-3,-3,0,1,-2,-1,1,-2,1,1,-2,-1,1,0,1,-2,1,2,0], [1,1,-1,1,0,0,1,-1,1,1,0,-2,1,-1,0,0,0,-1,0,1,-1,-1,0,1,0,0,0], [1,1,-1,1,0,0,1,0,1,1,0,-2,1,-1,0,0,0,-1,0,1,0,0,0,1,0,0,0], [-1,-1,1,-1,0,0,-1,0,-1,-1,1,2,-1,1,0,-1,0,1,0,-1,0,0,0,-1,0,0,0], [0,0,2,0,-1,1,-1,-2,0,0,1,1,2,2,3,0,-3,-1,2,-1,-1,1,-1,1,1,-1,-1], [2,2,-3,1,2,0,3,1,3,3,-1,-2,1,-2,-3,2,0,-1,0,1,1,-1,0,0,-1,-1,0], [3,4,-5,2,2,1,5,1,3,4,-2,-5,2,-4,-3,2,0,-1,0,1,1,-2,0,0,0,-1,0], [-1,-3,0,-1,1,-1,0,2,-3,-3,0,1,-4,-1,-1,-2,2,2,-2,0,1,-1,1,-2,0,2, 1], [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]]]; return result;