# Character: X9 # Comment: perm rep on 57 pts # Ind: 1 # Ring: Z # Sparsity: 72% # Maximum absolute entry: 3 # 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 := "L219 as 20 x 20 matrices\n"; result.generators := [ [[0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [-1,1,0,0,1,2,0,-1,0,1,0,1,0,0,1,0,-1,-1,-1,0], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0], [1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,-1,-1,0,0,0,-1,0,0,0,-1,0,-2,0,1,1,0], [1,-1,-1,0,0,-2,-1,1,0,0,0,-1,1,1,-1,1,1,0,0,0], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0], [0,0,-1,-1,0,-2,0,0,1,0,-1,-1,1,1,-1,0,1,0,0,0], [1,0,0,1,-1,0,0,1,0,-1,1,1,0,-1,0,-1,0,1,1,0], [1,-1,-1,0,1,-2,-2,1,0,0,-1,-1,1,1,-1,2,2,-1,-1,1], [-1,0,0,-1,1,0,0,-1,0,1,-1,0,0,1,0,1,0,-1,-1,0], [1,-1,-1,0,0,-2,-2,1,0,-1,-1,-1,1,0,0,0,1,0,0,1], [0,-1,0,1,1,1,-2,1,-1,1,0,2,1,-1,0,0,0,0,-1,0], [-1,1,0,-2,0,-1,2,-2,1,0,-1,-1,-1,1,0,-1,0,0,1,0], [0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,-1,0,1,1,-1]] , [[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,-1,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [-1,1,1,0,0,2,2,-1,0,1,1,1,-1,0,0,0,-1,0,0,-1], [1,-2,0,0,0,-1,-1,1,0,0,0,0,1,0,-1,1,1,0,0,0], [0,1,0,0,0,0,1,-1,0,0,0,0,-1,0,0,-1,0,0,1,0], [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0], [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,-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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,1,0], [1,-2,-1,0,1,-2,-2,0,0,0,-2,-1,1,1,-1,3,1,-1,-2,1], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0], [1,-1,0,0,-1,-2,0,1,0,-1,0,-1,0,0,-1,0,1,1,1,0], [0,-1,0,0,0,1,0,0,-1,1,0,0,0,0,0,2,0,-1,-1,0], [0,0,0,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0]]]; return result;