# Character: X4 # Comment: perm rep on 2304 pts # Ind: 0 # Ring: Q(i) # Sparsity: 79% # 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 := "TF42 as 27 x 27 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], [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], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0], [1/2-7/2*i,1/2-7/2*i,1-i,-3/2+5/2*i,1-i,-i,-3/2+5/2*i,1+i,1/2+13/2*i, -i,2+4*i,1+i,1/2+13/2*i,-5/2-7/2*i,3/2+5/2*i,2+4*i,1/2-5/2*i,2-3*i, -1,-5/2-7/2*i,3/2+5/2*i,0,0,1/2-5/2*i,2-3*i,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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0], [-9/2+5/2*i,-9/2+5/2*i,-1,11/2+1/2*i,-1,-1+i,11/2+1/2*i,-2*i,15/2-7/2*i, -1+i,3-5*i,-2*i,15/2-7/2*i,-7/2+7/2*i,5/2-7/2*i,3-5*i,-7/2+3/2*i, -4-i,0,-7/2+7/2*i,5/2-7/2*i,-1,0,-7/2+3/2*i,-4-i,0,0], [1-i,1-i,0,-2,0,0,-2,i,-2-i,0,0,i,-2-i,2,-1+i,0,1-i,i,0,2,-1+i,0,-1, 1-i,i,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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0], [7/2-1/2*i,7/2-1/2*i,1,-5/2-3/2*i,1,1,-5/2-3/2*i,-1+i,-9/2+1/2*i,1, -3+2*i,-1+i,-9/2+1/2*i,5/2-3/2*i,-5/2+3/2*i,-3+2*i,5/2-1/2*i,2+i, 0,5/2-3/2*i,-5/2+3/2*i,0,0,5/2-1/2*i,2+i,-1,0], [-1/2-7/2*i,-1/2-7/2*i,-i,-3/2+5/2*i,-i,-i,-3/2+5/2*i,1+i,3/2+9/2*i, -i,3+3*i,1+i,3/2+9/2*i,-3/2-5/2*i,3/2+5/2*i,3+3*i,1/2-5/2*i,1-3*i, 0,-3/2-5/2*i,3/2+5/2*i,0,0,1/2-5/2*i,1-3*i,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], [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0], [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], [25+7*i,31+3*i,4+4*i,-20-21*i,5+i,8,-19-23*i,-11+11*i,-37-4*i,8-3*i, -28+21*i,-7+4*i,-36-6*i,21,-25+9*i,-26+14*i,24+7*i,17+13*i,1-2*i, 22-4*i,-18+2*i,7+5*i,4-6*i,18+12*i,15+12*i,4+i,-2-5*i], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [22-5*i,25-10*i,5+2*i,-23-8*i,6-2*i,5-3*i,-23-10*i,-4+13*i,-29+13*i, 5-6*i,-12+27*i,-4+5*i,-29+10*i,14-8*i,-14+16*i,-14+21*i,20-4*i,18+2*i, -2-i,15-12*i,-14+9*i,7+i,-1-6*i,19+i,15+4*i,4-i,-2-4*i], [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], [1,2-i,0,-2-i,0,0,-2-i,2*i,-1,-i,2*i,0,-1,1,-1+i,i,2-i,0,0,1,-1,1, -i,1,0,0,0], [22-4*i,26-10*i,4+2*i,-24-9*i,5-2*i,5-3*i,-24-11*i,-4+14*i,-29+12*i, 5-6*i,-12+28*i,-4+5*i,-29+9*i,15-7*i,-15+16*i,-14+21*i,21-4*i,18+2*i, -1-i,15-11*i,-14+8*i,8+i,-7*i,19+2*i,15+4*i,4-i,-3-4*i], [-27/2-1/2*i,-31/2+5/2*i,-5/2-3/2*i,12+8*i,-7/2+1/2*i,-7/2+3/2*i,12+9*i, 9/2-15/2*i,18-3*i,-7/2+5/2*i,21/2-29/2*i,5/2-5/2*i,35/2-3/2*i,-8+2*i, 10-8*i,10-10*i,-23/2-1/2*i,-10-4*i,2+i,-10+4*i,9-2*i,-4-2*i,4*i, -11-4*i,-15/2-7/2*i,-7/2-1/2*i,1/2+5/2*i], [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], [25/2+45/2*i,41/2+47/2*i,-1/2+11/2*i,-29*i,7/2+11/2*i,11/2+11/2*i, 3-29*i,-31/2+1/2*i,-24-28*i,17/2+5/2*i,-69/2-7/2*i,-15/2-7/2*i,-43/2-57/2*i, 16+14*i,-24-11*i,-28-8*i,27/2+43/2*i,3+20*i,3-i,18+12*i,-14-11*i, 2+8*i,8-2*i,4+21*i,5/2+37/2*i,3/2+5/2*i,3/2-9/2*i]]]; return result;