# Character: X7 # Comment: perm rep on 120a pts # Ind: 1 # Ring: Z # Sparsity: 79% # Maximum absolute entry: 4 # 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 := "A9 as 35 x 35 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, 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], [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], [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0, 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], [0,0,0,0,0,0,1,0,0,0,0,0,-1,-1,0,1,0,-1,0,0,0,1,0,0,0,0,1,0,0,0,0, 0,0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,1], [1,0,0,-1,-1,0,-1,1,0,0,0,1,0,0,1,1,-1,0,0,0,0,0,1,0,0,-1,0,0,0,0, 0,0,0,0,0], [0,0,-1,0,-1,0,-1,1,-1,1,1,0,0,1,1,1,-1,0,0,1,0,-1,1,1,0,-1,-1,0,0, 1,0,-1,0,0,0], [-1,-1,-1,0,-1,1,0,2,-1,0,1,0,1,0,0,1,0,-1,0,1,0,-1,0,1,-1,0,-1,-1, 1,0,-1,-1,0,-1,1], [0,1,0,-1,0,0,-1,0,-1,0,0,0,-1,1,1,1,-1,0,0,0,1,0,1,0,0,0,0,0,0,0, 0,0,0,0,0], [1,0,1,0,0,-1,0,-1,1,0,-1,0,0,0,0,-1,0,1,1,0,-1,0,0,-1,1,0,1,1,-1, 0,0,0,0,1,-1], [0,0,-1,0,1,0,0,0,-1,1,0,0,0,1,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0], [-1,-1,-1,1,0,1,1,0,0,0,0,-1,1,-1,-1,0,1,-1,0,0,0,0,-1,0,-1,1,0,0, 1,0,-1,0,0,0,0], [0,0,2,0,0,1,1,-1,3,-2,-1,0,0,-3,-2,-1,2,1,-1,-1,0,1,-1,-2,0,1,2,-1, -1,0,0,1,-1,0,0], [-1,0,-2,0,1,-1,0,0,-3,2,1,-1,-1,2,1,1,-1,-2,0,0,1,0,1,2,-1,0,-1,1, 1,0,0,0,1,0,0], [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], [2,2,4,-1,1,-1,0,-3,4,-2,-3,1,-1,-1,-1,-2,-1,3,1,-2,-1,1,-1,-4,3,0, 3,1,-3,-1,1,1,0,2,-1], [0,-1,1,0,-1,1,1,1,2,-1,0,0,0,-3,-1,0,2,0,-1,0,0,1,0,-1,-1,0,1,-2, 0,0,0,0,-1,0,0], [-1,-1,-1,0,-1,1,0,2,-1,0,1,0,1,-1,0,1,1,-1,-1,1,0,0,0,1,-2,0,-1,-1, 1,0,-1,0,0,-1,1]] , [[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], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0, 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, 1,0], [0,-1,0,0,-1,0,1,1,0,0,0,0,0,-1,0,1,1,-1,0,0,0,1,0,1,-1,0,0,-1,1,0, 0,0,0,0,0], [0,0,-1,0,0,0,-1,1,-1,1,1,0,0,1,1,0,-1,0,0,1,0,-1,0,1,0,0,-1,0,0,0, 0,-1,0,0,1], [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], [-1,-1,0,0,-1,1,1,1,0,-1,0,0,1,-1,-1,1,2,-1,0,0,0,0,0,1,-1,0,-1,-2, 1,0,0,0,0,-1,0], [-1,0,-3,0,-1,0,-1,2,-4,2,2,-1,0,2,2,2,-1,-2,0,2,1,-1,1,3,-2,0,-2, 0,2,1,-1,-1,0,-1,1], [0,1,1,0,0,0,0,-1,1,-1,-1,0,0,0,0,0,0,1,0,0,0,0,0,-1,1,0,1,0,-1,0, 0,0,0,0,0], [-1,-1,0,0,-1,1,1,1,0,-1,0,0,0,-2,-1,1,2,-1,-1,0,0,1,0,1,-1,0,0,-2, 1,0,0,1,0,-1,0], [0,0,-1,0,0,-1,0,0,-1,1,1,0,0,1,1,0,0,-1,0,0,0,0,0,1,-1,0,-1,1,1,0, 0,0,0,0,0], [-1,0,-2,0,0,0,0,1,-3,2,2,-1,-1,1,1,1,0,-2,-1,1,1,0,1,2,-2,0,-1,0, 1,1,0,0,0,-1,1], [0,0,-1,1,1,0,0,-1,-1,1,0,-1,0,1,0,-1,0,0,0,0,0,0,0,0,0,1,0,1,0,0, 0,0,0,0,0], [0,0,2,0,0,1,1,-1,3,-2,-1,0,0,-3,-2,-1,2,1,-1,-1,0,1,-1,-2,0,1,2,-1, -1,0,0,1,-1,0,0], [1,0,1,0,0,-1,0,-1,1,0,-1,0,0,0,0,-1,0,1,1,0,-1,0,0,-1,1,0,1,1,-1, 0,0,0,0,1,-1], [1,1,3,0,1,0,0,-2,3,-2,-2,1,0,-1,-1,-2,0,3,0,-1,-1,0,-1,-3,2,0,2,0, -2,-1,1,1,0,1,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0, 0,0], [1,1,0,-1,0,-1,-1,0,-1,1,0,0,-1,1,1,0,-1,0,0,0,0,0,1,0,0,0,0,1,0,0, 0,0,0,0,0]]]; return result;