# Character: X3 # Comment: John Bray: http://web.mat.bham.ac.uk/spres/Spor/HN/ # Ind: 1 # Ring: C # Sparsity: 51% # 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 := "HN as 133 x 133 matrices\n"; result.generators := [ [[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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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-3/50*a+23/50*A,-11/50*a-9/50*A,3/25*a+2/25*A,1/50*a+19/50*A,4/25*a-4/25*A, 11/50*a+9/50*A,-7/50*a-3/50*A,3/50*a+1/25*A,9/50*a+1/50*A,-1/25*a-9/25*A, 7/50*a-7/50*A,6/25*a+3/50*A,9/50*a-7/25*A,-1/10*a+1/10*A,3/25*a+9/50*A, 3/50*a+6/25*A,-13/50*a-1/25*A,4/25*a+17/50*A,-3/50*a+4/25*A,-3/25*a-2/25*A, -7/25*a-11/50*A,1/10*a-1/10*A,-1/25*a+17/50*A,1/50*a+7/25*A,-1/5*a, 1/25*a-1/25*A,-1/25*a-4/25*A,-7/25*a-21/50*A,-3/50*a-6/25*A,-9/50*a-1/50*A, -3/50*a+4/25*A,-1/50*a-2/25*A], [1/4*a-1/8*A,1/2*A,-3/8*a+1/8*A,3/8*a+1/4*A,-1/4*a,-5/8*a-1/4*A,1/8*a-1/8*A, -5/8*a-1/4*A,-1/8*a+1/8*A,1/8*a,-3/8*a-1/8*A,3/8*a+1/8*A,-1/4*a-1/8*A, 1/4,-3/4*a-1/4*A,-1/8,3/4*a+3/8*A,3/8*a+1/4*A,3/8,-1/4*a,3/4*a+3/8*A, -1/8,1/8*a-1/4*A,-3/8,1/8*a+3/8*A,1/8*a-1/8*A,0,-3/4*a-1/2*A,1/8*a, -1/4*a-1/8*A,-1/8,-1/4,-1/4*a-1/8*A,-1/2*a-1/4*A,-7/8*a-3/8*A,-1/8*a+1/8*A, 3/4*a+3/8*A,1/2*a-1/4*A,1/4*a-1/8*A,-3/8*a+1/8*A,-1/2*a+1/8*A,0, 1/8*a-1/8*A,1/4*a+1/8*A,-1/4,-1/8*a+1/4*A,3/8*a+1/4*A,1/4*a-1/4*A, -1/8*a+1/8*A,3/8*a+1/8*A,1/4*a+1/8*A,-3/8*a,1/8,1/4*A,1/4*a+3/8*A, 0,1/8*a+1/4*A,1/2*a+1/4*A,-1/2*a-1/4*A,-1/4,1/8*a-1/8*A,-1/8*a,3/8*a+1/2*A, 3/8*a+1/8*A,-1/4*A,3/4*a+1/2*A,1/8*a+3/8*A,-1/4,1/4*a+1/8*A,-1/8*a-1/4*A, 1/4*A,1/4,1/4,-1/8*a+1/4*A,-3/8*a,-1/8*a+1/4*A,3/8*a+1/8*A,1/25*a-1/25*A, -3/50*a-1/25*A,-3/25*a-9/50*A,9/50*a+11/50*A,-3/25*a-9/50*A,2/25*a+3/25*A, 3/50*a+1/25*A,-11/50*a-2/25*A,2/25*a-2/25*A,1/5*a+1/10*A,9/50*a+11/50*A, 1/25*a+4/25*A,-7/50*a-13/50*A,3/25*a+7/25*A,19/50*a+13/25*A,2/25*a+21/50*A, 3/25*a+2/25*A,2/25*a+11/50*A,8/25*a+7/25*A,3/25*a+2/25*A,-1/5*A, 3/50*a+7/50*A,-1/50*a-9/50*A,1/10,-3/50*a+3/50*A,9/50*a+21/50*A, 3/25*a+7/25*A,3/25*a+2/25*A,-1/25*a-4/25*A,1/50*a+2/25*A,3/50*a+6/25*A, -7/50*a-13/50*A,-1/50*a+3/25*A,-6/25*a-4/25*A,1/25*a+4/25*A,1/25*a-1/25*A, -1/50*a-2/25*A,1/10*A,-2/25*a-1/50*A,-1/25*a+7/50*A,-4/25*a-6/25*A, -6/25*a-13/50*A,1/25*a-1/25*A,9/50*a+1/50*A,-9/50*a-1/50*A,-1/10*a, 4/25*a+6/25*A,-9/50*a-21/50*A,0,-3/50*a+3/50*A,-1/25*a-3/50*A,21/50*a+19/50*A, 1/25*a+4/25*A,-2/25*a+2/25*A,-4/25*a-6/25*A,-1/50*a+3/25*A]]]; return result;