# Character: X3 # Comment: perm rep on 1539 pts # Ind: 0 # Ring: Q(w) # Sparsity: 81% # 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 := "U38 as 57 x 57 matrices\n"; result.generators := [ [[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], 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9*w+4*W,-2/3*w+5/3*W,7*w+3*W,-10/3*w-14/3*W,2*w-5*W,2*w-6*W], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [-5*w-37*W,-16*w-28*W,-32/3*w+59/3*W,-19/3*w+43/3*W,-2/3*w-46/3*W, -7/3*w+37/3*W,-97/3*w-80/3*W,13/3*w-19/3*W,-30*w-8*W,83/3*w+115/3*W, -5*w+5*W,34/3*w+62/3*W,-8*w-15*W,46/3*w+62/3*W,-40/3*w-119/3*W,w-17*W, 47/3*w+28/3*W,-5/3*w-49/3*W,11/3*w+97/3*W,19/3*w-10/3*W,-31/3*w-53/3*W, w+4*W,13*w+27*W,-46/3*w-50/3*W,-32/3*w-1/3*W,-3*w+3*W,59/3*w+97/3*W, 37*w+2*W,-44/3*w-46/3*W,-2/3*w+35/3*W,24*w+6*W,-7*w+14*W,12*w+20*W, 20/3*w+25/3*W,25*w+2*W,61/3*w+11/3*W,28*w+9*W,-74/3*w-100/3*W,-67/3*w+64/3*W, 28/3*w+50/3*W,53/3*w+40/3*W,-3*w-34*W,22*w+18*W,-20,2/3*w+16/3*W, 16/3*w+2/3*W,-6*w-12*W,52/3*w+20/3*W,-6*w-19*W,-18*w+21*W,-34/3*w+28/3*W, 24*w-W,14/3*w+34/3*W,20*w,-53/3*w-34/3*W,-5*w-20*W,-9*w-31*W]]]; return result;