# Character: X4+X5+X6 # Comment: perm rep on 78 pts # Ind: 1 # Irred-dim: 12 # Ring: Z # Sparsity: 70% # Maximum absolute entry: 7 # 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 := "L213 as 36 x 36 matrices\n"; result.generators := [ [[0,0,0,0,0,0,0,0,-1,2,0,0,1,0,-1,0,0,0,2,-1,1,1,0,-1,0,0,1,0,-1,0, 1,0,-1,-1,0,0], [0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0], [1,0,0,1,0,0,1,0,0,0,-1,0,-1,0,-1,1,1,1,1,-1,0,0,0,0,1,-1,1,-1,0,0, 0,1,0,0,0,0], [0,-1,0,0,0,-1,1,1,-1,1,0,0,1,1,-1,0,0,-1,1,0,1,1,-1,1,-1,0,1,0,-1, 0,0,1,0,0,1,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0], [1,-1,1,1,1,0,2,1,-1,-2,1,0,-2,1,-2,2,0,-1,0,-1,-1,1,-2,2,0,-1,0,-1, -1,1,0,1,1,2,1,1], [0,0,-1,0,0,-1,0,0,-1,1,0,0,1,0,0,0,0,0,1,0,1,0,0,0,-1,0,1,0,0,0,0, 0,-1,0,0,0], [2,0,0,1,0,0,1,1,-2,6,0,0,3,1,-2,-1,0,0,6,-2,3,2,0,-1,-1,0,3,0,-3, -1,2,2,-2,-2,0,0], [1,0,1,1,1,2,1,0,0,5,0,1,3,0,-2,-1,0,-1,4,-2,1,2,0,-2,0,0,2,1,-3,-1, 2,1,-1,-2,-1,0], [1,0,0,0,1,0,1,1,-1,3,0,0,2,0,-2,0,0,-1,4,-1,2,1,-1,0,-1,0,2,0,-2, 0,1,1,-1,-1,0,0], [3,1,0,2,0,0,2,0,-2,4,-1,0,1,0,-3,1,1,1,6,-3,2,2,0,-1,1,-1,3,-2,-2, 0,2,2,-2,-1,0,0], [1,1,0,1,0,0,0,-1,1,1,-2,0,-1,-1,0,1,2,3,2,-1,0,-1,1,-2,2,-1,1,-1, 1,0,0,0,-1,-1,-1,-1], [2,-1,1,1,1,1,3,1,-1,0,1,0,-1,2,-3,2,0,-1,1,-2,0,1,-2,1,0,-1,1,-1, -2,1,1,1,1,2,1,1], [-1,0,-1,-1,-1,-2,-1,-1,0,-3,-1,0,-1,-2,2,0,1,1,-3,2,0,-2,0,0,0,0, -1,0,3,1,-2,-1,0,1,0,-1], [0,0,1,0,0,1,0,0,1,-1,0,0,-1,0,0,0,0,0,-1,0,-1,0,0,0,1,0,-1,0,0,0, 0,0,1,1,0,0], [0,0,0,0,0,-1,1,0,0,-3,-1,0,-2,0,0,2,1,1,-1,0,-1,-1,-1,0,1,-1,0,-1, 1,1,-1,0,1,1,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0, 0,0,0], [2,1,1,1,0,1,1,0,0,1,-1,0,0,0,-2,0,1,1,3,-1,1,1,0,-1,1,-1,1,-1,-1, 0,1,1,-1,-1,0,0], [3,0,1,2,1,2,2,0,-1,5,-1,1,2,2,-3,0,1,1,7,-4,2,2,0,-1,1,-1,3,-1,-4, -1,2,2,-1,-2,0,0]] , [[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], [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,-1,2,0,0,1,0,-1,0,0,0,2,-1,1,1,0,-1,0,0,1,0,-1,0, 1,0,-1,-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], [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], [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0], [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,-1,1,0,-1,0,0,0,0,0,-1,1,1,0,1,-1,1,0,-1,0,0,0,1,-1,0,1, 0,0,0,0,0,0], [0,0,0,0,-1,0,-1,0,0,1,0,0,0,0,0,0,-1,0,0,0,0,0,1,0,0,1,0,0,0,0,1, 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], [0,0,0,0,0,0,0,0,0,1,1,0,1,1,0,-1,-1,-1,0,0,1,0,0,1,-1,1,0,0,-1,0, 0,0,0,0,0,1], [0,0,0,0,1,0,1,0,0,0,0,0,0,0,-1,1,1,0,0,-1,0,0,-1,-1,1,0,1,0,0,0,0, 0,0,0,0,0], [1,0,0,1,0,0,1,1,0,-2,0,0,-2,1,0,1,0,1,-1,0,-1,-1,0,1,0,-1,0,-1,1, 0,0,0,1,1,1,1], [2,-1,0,2,1,0,3,1,-1,-3,-1,0,-3,1,-2,3,2,1,1,-1,-1,0,-2,1,1,-3,1,-2, 0,1,-1,1,1,2,1,0], [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], [-2,-1,0,-1,0,0,0,0,1,-2,2,0,-1,1,1,-1,-2,-2,-3,2,-1,0,0,2,-1,1,-2, 1,0,0,-1,0,1,1,1,1], [-1,0,0,-1,-1,-1,-2,0,0,0,0,0,0,0,1,-1,-1,0,-2,1,0,-1,1,1,-1,1,-1, 0,1,0,0,-1,0,0,0,0], [0,0,-1,0,0,-1,0,0,0,-4,0,0,-1,0,2,0,0,1,-3,2,-1,-2,0,1,-1,-1,-1,0, 2,0,-2,-1,1,1,0,0], [-1,0,0,0,0,-2,1,0,-1,1,0,0,1,-1,-1,1,1,0,2,0,2,1,-1,-1,0,0,2,0,0, 1,0,0,-1,-1,0,-1], [1,0,0,0,1,0,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0,0,-1,-1,0,-1,1,0,0,0,0, 0,0,0,0,0], [3,0,1,2,0,1,2,1,-2,3,0,0,1,1,-3,1,0,-1,5,-2,1,3,-1,-1,0,-1,2,-1,-3, 0,2,2,-1,0,0,0], [0,1,0,0,1,0,1,0,-1,4,1,0,3,0,-2,0,1,-1,3,-2,2,1,-1,-2,0,1,2,0,-2, 0,1,0,-1,-1,-1,0], [0,0,-1,0,0,-1,0,0,-1,1,-1,0,1,-1,0,0,1,0,2,0,1,0,0,-1,0,0,1,0,0,0, 0,0,-1,-1,-1,-1], [-1,1,-1,0,0,0,-2,-1,2,-3,-1,0,-2,-1,3,0,1,2,-3,0,-2,-3,1,-1,1,0,-1, 0,3,-1,-1,-2,1,0,-1,0], [1,-1,0,1,1,-1,3,1,-1,0,0,0,0,1,-2,2,1,0,2,-1,1,1,-2,0,0,-1,2,-1,-1, 1,0,1,0,1,1,0], [-2,1,0,-1,0,-1,-2,-1,1,-1,-1,0,1,-2,3,-1,0,1,-2,1,0,-2,1,-1,0,1,-1, 1,2,0,-1,-2,0,-1,-1,-1], [0,-1,0,0,0,0,2,1,0,-1,1,0,-1,2,-1,0,-1,-2,0,0,0,1,-1,2,-1,0,0,0,-1, 1,0,1,1,1,1,1]]]; return result;