# Character: X3 # Comment: perm rep on 728 pts - LLL'ed # Ind: 1 # Ring: Z # Sparsity: 75% # Maximum absolute entry: 10 # 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 := "O73 as 91 x 91 matrices\n"; result.generators := [ [[0,0,0,0,0,0,0,-1,-1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,-1,1,0,0, 1,0,0,0,1,1,0,-1,-1,0,0,-1,0,0,0,0,0,0,0,0,-1,0,0,-1,-1,0,0,-1,0, -1,-1,0,0,0,0,0,1,-1,-1,-1,0,0,0,-1,-1,0,0,0,-1,0,0,0,1,0,0,0,-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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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, 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-2,-5,2,-3,1,1,0,4,4,1,-3,0,2,-2,-6,0,2,2,1,-1,-2,-3,-2,3,1,0,2, 0,-3,1,0,2,-3,1,0,-4,2,1], [4,0,-4,0,1,0,-1,3,3,2,-3,-1,-2,1,4,-1,4,-1,4,1,-2,-2,1,-1,5,6,0,-3, 2,1,4,-4,-2,1,0,-1,3,-1,1,0,-1,5,-2,-2,2,1,-10,1,9,-8,-6,-2,4,5, 5,-1,4,-1,-2,-2,-5,-2,-3,2,-3,-2,1,6,3,0,1,1,-2,0,5,1,-2,2,1,-3, -1,6,2,0,-1,3,2,-2,6,-3,-2], [-5,1,5,-1,-3,-1,2,0,0,-1,5,2,0,-3,-2,2,-3,1,-3,-4,2,3,-2,1,-6,-5, 0,3,-4,-1,-4,3,3,-2,-2,1,-4,1,1,2,0,-6,2,3,-1,-2,10,1,-7,7,5,3,-4, -5,-5,2,-3,0,2,2,7,4,1,-3,1,4,-3,-6,-2,2,2,2,1,-2,-4,-2,3,-1,0,4, 1,-5,0,-3,2,-2,-3,3,-5,4,3], [3,1,-3,4,0,0,-1,0,0,-2,-4,-1,4,6,-4,-2,-2,1,-1,6,-3,-1,0,-1,3,-1, 1,2,4,-1,1,1,-2,2,1,-1,1,2,1,-1,0,0,0,-3,-5,3,-1,0,-1,-2,-3,-1,-5, 3,-2,-3,-6,4,-3,0,-5,-4,5,0,4,-6,4,-2,-2,-5,-5,-5,2,1,1,0,-3,-3, -4,-2,1,-1,-1,5,-2,-3,2,-3,0,2,-2], [-2,-1,1,-1,0,1,1,0,0,0,1,1,-1,-2,-1,2,0,0,-1,-3,2,0,0,2,-1,-2,-1, 0,-2,0,-1,1,1,-2,0,-1,-2,-1,1,0,0,-1,0,1,2,-1,2,2,-2,1,1,1,0,-1, -1,1,1,0,0,0,3,2,-1,-1,-1,1,-2,-2,0,2,2,2,0,-2,0,-1,1,-1,0,0,-2, -1,0,-2,1,0,-1,0,0,1,1], [5,-1,-5,1,3,0,-2,0,0,1,-5,-2,0,3,2,-2,3,-1,3,4,-2,-3,2,-1,6,5,0,-3, 4,1,4,-3,-3,2,2,-1,4,-1,-1,-2,0,6,-2,-3,1,2,-10,-1,7,-7,-5,-3,4, 5,5,-2,3,0,-2,-2,-7,-4,-1,3,-1,-4,3,6,2,-2,-2,-2,-1,2,4,2,-3,1,0, -4,-1,5,0,3,-2,2,3,-3,5,-4,-3], [-2,0,3,1,-1,1,1,0,0,-1,2,1,-1,-1,-2,1,-2,0,0,-2,2,1,-1,0,-3,-1,0, 0,-2,-1,-1,3,0,-1,0,0,-3,1,0,1,0,-4,2,2,-1,-1,5,0,-4,2,2,0,-2,-2, -3,2,-3,1,1,0,3,2,2,-2,1,1,-1,-4,-1,1,1,-1,0,0,-1,1,2,0,0,2,1,-2, -1,0,1,-2,1,1,-3,2,1], [1,0,0,-2,-1,-2,0,2,2,-1,1,0,-2,-2,2,1,2,0,3,-1,1,3,0,2,0,3,-1,-3, -2,0,2,-2,-1,-3,-2,1,1,-4,0,0,-1,0,-1,2,3,0,-3,3,3,-2,-2,0,2,1,-1, -1,4,-4,-1,1,-2,2,-3,-1,-2,1,-3,2,0,1,1,5,-1,-1,3,-1,2,2,2,-1,-1, 2,2,-4,2,3,-2,-1,3,0,-1], [0,2,0,1,-2,-3,-1,1,2,1,2,0,2,0,0,-1,-2,1,-3,0,-1,1,-1,-1,-1,-3,1, 5,0,-1,-3,-3,2,0,-1,-1,-1,2,2,2,-1,0,3,-1,-4,1,2,0,-1,3,1,5,-2,-2, 2,1,-2,0,1,2,4,0,2,-1,3,1,1,-1,0,0,0,0,1,0,-1,0,-1,-1,-2,2,1,-3, 0,-3,-1,0,-4,4,-2,2,2], [4,1,-5,2,1,-1,-2,4,4,0,-3,-1,0,3,0,-2,3,0,2,2,-2,-1,1,0,5,3,0,1,2, 1,3,-5,-1,0,0,-3,1,-1,3,1,-1,4,0,-3,-1,2,-7,3,5,-7,-6,1,0,5,5,-1, 2,1,-2,0,-4,-2,0,2,1,-4,2,3,2,0,-1,2,1,1,6,1,-4,-2,-2,-3,-2,3,0, -3,-1,3,-1,-1,5,0,-1]]]; return result;