# Character: X7 # Comment: perm rep on 208 pts # Ind: 1 # Ring: C # Sparsity: 84% # 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 := "U34 as 39 x 39 matrices\n"; result.generators := [ [[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], [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], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1, 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, 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, 0,1,0,0,0,0], [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, 0,0,0,1,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [-41/55*a+26/55*A,41/55*a-26/55*A,6/5*a+4/5*A,-114/55*a-86/55*A,-6/5*a-4/5*A, 27/11*a+14/11*A,114/55*a+86/55*A,-46/55*a+1/55*A,3/11*a+15/11*A, -27/11*a-14/11*A,2/55*a+43/55*A,46/55*a-1/55*A,-3/11*a-15/11*A,-34/55*a+39/55*A, 31/55*a+34/55*A,-2/55*a-43/55*A,-6/5*a-4/5*A,0,0,34/55*a-39/55*A, -31/55*a-34/55*A,31/55*a+34/55*A,81/55*a+9/55*A,6/5*a+4/5*A,24/11*a+10/11*A, -1/55*a-49/55*A,5/11*a+3/11*A,-48/55*a-42/55*A,-31/55*a-34/55*A, -81/55*a-9/55*A,1,0,-24/11*a-10/11*A,1/55*a+49/55*A,-5/11*a-3/11*A, 0,48/55*a+42/55*A,0,0], [-7/55*a-13/55*A,7/55*a+13/55*A,-3/5*a-2/5*A,57/55*a+43/55*A,3/5*a+2/5*A, -8/11*a-7/11*A,-57/55*a-43/55*A,-32/55*a-28/55*A,-7/11*a-13/11*A, 8/11*a+7/11*A,-1/55*a-49/55*A,32/55*a+28/55*A,7/11*a+13/11*A,17/55*a-47/55*A, -43/55*a-17/55*A,1/55*a+49/55*A,-2/5*a+2/5*A,0,0,-17/55*a+47/55*A, 43/55*a+17/55*A,12/55*a-17/55*A,-13/55*a+23/55*A,2/5*a-2/5*A,-12/11*a-5/11*A, 28/55*a+52/55*A,3/11*a+4/11*A,24/55*a+21/55*A,-12/55*a+17/55*A,13/55*a-23/55*A, 0,1,12/11*a+5/11*A,-28/55*a-52/55*A,-3/11*a-4/11*A,0,-24/55*a-21/55*A, 0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,0], [-26/11*a-20/11*A,26/11*a+20/11*A,-A,-13/11*a+1/11*A,A,18/11*a+2/11*A, 13/11*a-1/11*A,-1/11*a-5/11*A,2/11*a-12/11*A,-18/11*a-2/11*A,-10/11*a-6/11*A, 1/11*a+5/11*A,-2/11*a+12/11*A,-6/11*a-8/11*A,10/11*a-5/11*A,10/11*a+6/11*A, A,0,0,6/11*a+8/11*A,-10/11*a+5/11*A,-1/11*a-5/11*A,24/11*a+10/11*A, -A,27/11*a+14/11*A,5/11*a+14/11*A,-4/11*a-9/11*A,-13/11*a+1/11*A, 1/11*a+5/11*A,-24/11*a-10/11*A,0,0,-27/11*a-14/11*A,-5/11*a-14/11*A, 4/11*a+9/11*A,1,13/11*a-1/11*A,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0, 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, 0,0,0,0,1,0], [1,-1,-1,1,1,2*a+A,-1,1,a+2*A,-2*a-A,a+3*A,-1,-a-2*A,2*A,0,-a-3*A, 1,0,0,-2*A,0,0,a-A,-1,2*a+A,-A,-A,1,0,-a+A,0,0,-2*a-A,A,A,0,-1,0, 1]] , [[0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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], [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0, 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, 0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0, 0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0, 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], [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 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, 0,0,1,0,0,0], [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, 0,0,0,0,1,0], [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, 0,0,0,0,0,1], [339/55*a+387/110*A,-64/55*a+109/55*A,27/10*a+63/10*A,296/55*a-291/55*A, 63/10*a+21/5*A,-51/11*a-15/22*A,34/55*a+456/55*A,-177/110*a+17/110*A, -35/11*a+233/22*A,113/22*a-9/11*A,897/55*a+1273/55*A,281/55*a+239/55*A, -183/22*a-409/22*A,481/55*a+2093/110*A,-479/55*a-371/55*A,-859/110*a-1273/55*A, 23/10*a+1/5*A,-a+A,-11/2*a-17/2*A,-1347/110*a-1129/55*A,259/55*a+27/110*A, 71/55*a+69/55*A,-604/55*a-2047/110*A,97/10*a+39/5*A,-175/22*a+30/11*A, -201/55*a-1273/110*A,-7/11*a-123/11*A,-78/55*a-549/110*A,-527/110*a-289/55*A, 604/55*a+947/110*A,-13/2*a-25/2*A,-13/2*a-2*A,93/11*a+39/22*A,127/110*a+279/55*A, 40/11*a+103/22*A,3/2*a-9/2*A,-417/55*a+82/55*A,-4*a-3*A,-a-11/2*A ], [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], [-477/110*a-109/55*A,101/55*a-1/55*A,-4/5*a-17/10*A,-254/55*a+39/55*A, -37/10*a-23/10*A,63/22*a+9/11*A,34/55*a-149/55*A,49/55*a+17/110*A, 73/22*a-32/11*A,-85/22*a-7/22*A,-423/55*a-487/55*A,-159/55*a-146/55*A, 35/11*a+141/22*A,-303/110*a-356/55*A,291/55*a+179/55*A,241/110*a+919/110*A, -27/10*a-13/10*A,-A,3*a+7/2*A,633/110*a+877/110*A,-307/110*a-14/55*A, 16/55*a+14/55*A,607/110*a+434/55*A,-53/10*a-27/10*A,111/22*a-17/22*A, 93/110*a+216/55*A,-7/11*a+42/11*A,9/110*a+83/55*A,243/110*a+247/110*A, -717/110*a-214/55*A,3*a+11/2*A,7/2*a+3/2*A,-111/22*a-19/11*A,17/110*a-157/110*A, -41/22*a-20/11*A,-2*a+3/2*A,298/55*a+27/55*A,3*a+2*A,1/2*a+2*A], [-26/11*a-31/11*A,-7/11*a-24/11*A,-2*a-5*A,9/11*a+67/11*A,-2*a-4*A, -4/11*a-20/11*A,-31/11*a-89/11*A,10/11*a+6/11*A,-31/11*a-133/11*A, 4/11*a+31/11*A,-98/11*a-204/11*A,-32/11*a-50/11*A,75/11*a+188/11*A, -72/11*a-184/11*A,32/11*a+39/11*A,87/11*a+237/11*A,-a-2*A,-A,4*a+9*A, 83/11*a+195/11*A,1/11*a+27/11*A,-1/11*a+6/11*A,79/11*a+197/11*A, -3*a-4*A,-6/11*a-63/11*A,49/11*a+135/11*A,40/11*a+134/11*A,20/11*a+45/11*A, 23/11*a+49/11*A,-35/11*a-54/11*A,5*a+13*A,a-A,-16/11*a-3/11*A,-16/11*a-47/11*A, -18/11*a-35/11*A,2*a+7*A,2/11*a-45/11*A,2*a+3*A,2*a+6*A], [-29/22*a-23/11*A,-2/11*a-21/11*A,-2*a-11/2*A,23/11*a+82/11*A,-3/2*a-5/2*A, -7/22*a-12/11*A,-34/11*a-104/11*A,6/11*a-17/22*A,-101/22*a-148/11*A, 29/22*a+79/22*A,-94/11*a-206/11*A,-28/11*a-41/11*A,67/11*a+373/22*A, -137/22*a-183/11*A,28/11*a+41/11*A,221/22*a+511/22*A,-1/2,-a-2*A, 3*a+15/2*A,159/22*a+399/22*A,-1/22*a+25/11*A,-5/11*a-3/11*A,141/22*a+182/11*A, -5/2*a-9/2*A,-27/22*a-135/22*A,105/22*a+136/11*A,46/11*a+131/11*A, 35/22*a+49/11*A,65/22*a+105/22*A,-53/22*a-50/11*A,5*a+25/2*A,1/2, -17/22*a+7/11*A,-39/22*a-107/22*A,-15/22*a-32/11*A,2*a+13/2*A,-12/11*a-49/11*A, a+2*A,5/2*a+6*A], [-244/55*a-207/110*A,189/55*a+131/55*A,3/10*a-3/10*A,-331/55*a-159/55*A, -23/10*a+4/5*A,37/11*a+29/22*A,221/55*a+159/55*A,197/110*a+83/110*A, 64/11*a+79/22*A,-107/22*a-20/11*A,-247/55*a+52/55*A,-126/55*a-14/55*A, -7/22*a-35/22*A,19/55*a+267/110*A,269/55*a+36/55*A,-111/110*a-217/55*A, -13/10*a+4/5*A,0,1/2*a-3/2*A,237/110*a-106/55*A,-214/55*a-127/110*A, -61/55*a-74/55*A,144/55*a-243/110*A,-47/10*a-9/5*A,177/22*a+52/11*A, -69/55*a-217/110*A,-40/11*a-46/11*A,-67/55*a-21/110*A,177/110*a-36/55*A, -309/55*a-197/110*A,-1/2*a-5/2*A,7/2*a+2*A,-72/11*a-71/22*A,-27/110*a-29/55*A, -4/11*a+15/22*A,7/2,342/55*a+148/55*A,2*a,-1/2*A], [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], [373/55*a+529/110*A,-98/55*a+38/55*A,19/10*a+51/10*A,357/55*a-162/55*A, 71/10*a+27/5*A,-53/11*a-13/22*A,-27/55*a+327/55*A,-259/110*a-151/110*A, -45/11*a+177/22*A,117/22*a-10/11*A,784/55*a+1016/55*A,322/55*a+323/55*A, -163/22*a-353/22*A,422/55*a+1701/110*A,-443/55*a-257/55*A,-633/110*a-1016/55*A, 31/10*a+12/5*A,-a+A,-11/2*a-17/2*A,-1229/110*a-933/55*A,223/55*a-201/110*A, 52/55*a+18/55*A,-588/55*a-1909/110*A,89/10*a+28/5*A,-181/22*a+15/11*A, -172/55*a-1181/110*A,2/11*a-100/11*A,-61/55*a-423/110*A,-489/110*a-238/55*A, 588/55*a+809/110*A,-13/2*a-25/2*A,-13/2*a-2*A,96/11*a+69/22*A,69/110*a+233/55*A, 31/11*a+57/22*A,3/2*a-9/2*A,-434/55*a+19/55*A,-4*a-3*A,-a-11/2*A ], [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], [-32/11*a+5/11*A,32/11*a+39/11*A,2*a+5*A,-82/11*a-102/11*A,-2*a+A, 45/11*a+27/11*A,49/11*a+91/11*A,3/11*a+4/11*A,93/11*a+146/11*A,-56/11*a-49/11*A, 30/11*a+172/11*A,-3/11*a+29/11*A,-60/11*a-168/11*A,51/11*a+167/11*A, 25/11*a-18/11*A,-96/11*a-227/11*A,-2*a-A,-1,-a-6*A,-40/11*a-167/11*A, -36/11*a-37/11*A,3/11*a+4/11*A,-28/11*a-151/11*A,-2*a+2*A,84/11*a+90/11*A, -48/11*a-119/11*A,-65/11*a-127/11*A,-27/11*a-47/11*A,-3/11*a-37/11*A, -38/11*a+30/11*A,-3*a-10*A,3*a+2*A,-62/11*a-35/11*A,26/11*a+53/11*A, -1/11*a+28/11*A,-4*a-6*A,71/11*a+69/11*A,a-A,-3*a-6*A]]]; return result;