# Character: X2 # Comment: complex conjugate # Ind: 0 # Ring: Z(w) # Sparsity: 80% # 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 := "S63 as 13 x 13 matrices\n"; result.generators := [ [[-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,-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,-1,0,0,0,0,0,0,0,0], [0,0,0,0,0,-1,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0,0], [0,-W,w,1,0,-w-2*W,0,1,0,0,0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,1,0], [-w,3*w,3*w+2*W,w,W,2*w,w,0,-w,w+2*W,1,-w-2*W,0], [0,0,0,0,0,0,0,0,0,1,0,0,0], [-1,1,-w+W,1,w,2*W,w+2*W,0,-w-2*W,0,0,0,1]] , [[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], [0,0,0,0,1,0,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0,0,0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0,0], [0,0,0,0,0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0], [0,-1,0,-1,0,-1,0,-1,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,1,0,0], [1,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,1], [1,W,1,-w+W,-w,-2*w,-w,-w,w,-w,w,-1,w], [-w,w,0,-1,0,-1,0,0,0,0,0,-W,0]]]; return result;