# Character: X8 # Comment: split 102, seed with A5 x A5 # Ind: 1 # Ring: C # Sparsity: 77% # 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 := "S44 as 51 x 51 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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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, 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13*a+6*A,-10*a-4*A,-36*a-15*A,-21*a-10*A,-41*a-14*A,-34*a-14*A,-3*a-2*A, -1,16*a+7*A,-26*a-10*A,a,-a,-33*a-12*A,-13*a-5*A,a+2*A,11*a+3*A, -31*a-12*A,-18*a-7*A,-11*a-4*A,11*a+4*A,9*a+3*A,19*a+8*A,-31*a-12*A, 1,-51*a-21*A,-28*a-12*A,30*a+10*A,39*a+14*A], [5*a+7*A,30*a+8*A,80*a+31*A,15*a+2*A,7*a+6*A,35*a+11*A,13*a+8*A,28*a+9*A, -29*a-12*A,-14*a-8*A,11*a+10*A,22*a+7*A,61*a+21*A,-70*a-26*A,-35*a-11*A, -26*a-9*A,28*a+10*A,-63*a-28*A,8*a+4*A,3*a+2*A,9*a+4*A,-24*a-12*A, 35*a+11*A,20*a+11*A,-14*a-5*A,-54*a-25*A,-32*a-17*A,-59*a-18*A,-50*a-20*A, -5*a-4*A,a+2*A,24*a+12*A,-39*a-14*A,-1,-2*a,-49*a-18*A,-19*a-8*A, 2*a+4*A,17*a+5*A,-45*a-17*A,-27*a-9*A,-16*a-6*A,16*a+5*A,13*a+4*A, 28*a+13*A,-46*a-18*A,2,-75*a-31*A,-42*a-18*A,45*a+15*A,57*a+20*A ], [9/2*a-9/2*A,84*a+73/2*A,411/2*a+155/2*A,45*a+22*A,25/2*a+1/2*A,189/2*a+79/2*A, 55/2*a+7*A,153/2*a+32*A,-74*a-27*A,-30*a-15/2*A,39/2*a,59*a+24*A, 163*a+66*A,-183*a-141/2*A,-95*a-39*A,-139/2*a-55/2*A,73*a+28*A,-156*a-55*A, 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-28*a-9*A,65/2*a+14*A,87/2*a+18*A], [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], [1/2*a-21/2*A,62*a+61/2*A,293/2*a+109/2*A,34*a+21*A,15/2*a-9/2*A,139/2*a+67/2*A, 37/2*a+2*A,111/2*a+26*A,-52*a-18*A,-19*a+1/2*A,21/2*a-9*A,43*a+20*A, 117*a+51*A,-131*a-103/2*A,-69*a-31*A,-101/2*a-43/2*A,52*a+19*A,-109*a-33*A, 29/2*a+4*A,7/2*a-1/2*A,31/2*a+11/2*A,-79/2*a-19/2*A,69*a+31*A,31*a+9/2*A, -26*a-21/2*A,-185/2*a-27*A,-51*a-17/2*A,-233/2*a-53*A,-181/2*a-65/2*A, -11/2*a+3/2*A,-4*A,79/2*a+19/2*A,-74*a-29*A,1/2*a,-6*a-5*A,-92*a-75/2*A, -69/2*a-23/2*A,-3/2*a-7*A,34*a+16*A,-165/2*a-61/2*A,-101/2*a-43/2*A, -61/2*a-25/2*A,63/2*a+14*A,51/2*a+23/2*A,47*a+25/2*A,-169/2*a-61/2*A, -a+5/2*A,-134*a-45*A,-73*a-23*A,88*a+79/2*A,110*a+93/2*A], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0], [-3*a+5*A,-64*a-28*A,-156*a-59*A,-34*a-17*A,-9*a+A,-73*a-32*A,-21*a-5*A, -59*a-25*A,56*a+20*A,22*a+4*A,-14*a+2*A,-45*a-19*A,-124*a-51*A,139*a+54*A, 72*a+30*A,53*a+22*A,-55*a-20*A,118*a+40*A,-16*a-5*A,-5*a-A,-17*a-6*A, 44*a+14*A,-72*a-30*A,-34*a-9*A,28*a+11*A,101*a+34*A,57*a+15*A,123*a+52*A, 97*a+36*A,7*a+A,-a+2*A,-43*a-13*A,79*a+31*A,-a,6*a+4*A,98*a+39*A, 37*a+13*A,a+4*A,-35*a-15*A,89*a+33*A,54*a+22*A,33*a+13*A,-33*a-14*A, -27*a-11*A,-52*a-17*A,90*a+33*A,2*a-A,145*a+52*A,79*a+27*A,-92*a-38*A, -116*a-47*A], [7/2*a+10*A,-13/2*a-15/2*A,-19/2*a-3*A,-4*a-7*A,3/2*a+6*A,-13/2*a-7*A, 9/2*A,-5*a-9/2*A,3*a,-1/2*a-11/2*A,4*a+23/2*A,4,-9*a-7*A,17/2*a+9/2*A, -6,9/2*a+4*A,-3*a-A,5*a-5*A,3/2*A,1/2*a+2*A,-1/2*a+A,1/2*a-4*A,6, 1/2*a+11/2*A,-3/2,3*a-11/2*A,1/2*a-15/2*A,10*a+21/2*A,11/2*a+A,-1/2*a-3*A, a+3*A,-1/2*a+4*A,6*a+4*A,a+3/2*A,a+2*A,13/2*a+7/2*A,3/2*a-A,2*a+11/2*A, 3,11/2*a+2*A,9/2*a+4*A,5/2*a+A,-3*a-5/2*A,-5/2*a-2*A,-3/2*a+7/2*A, 11/2*a+A,-1/2*a-5/2*A,7*a-A,3*a-2*A,-15/2*a-13/2*A,-17/2*a-13/2*A ], [-5/2*a+24*A,-285/2*a-141/2*A,-683/2*a-128*A,-79*a-48*A,-31/2*a+12*A, -323/2*a-77*A,-44*a-9/2*A,-130*a-119/2*A,122*a+43*A,91/2*a+1/2*A, -24*a+41/2*A,-99*a-46*A,-272*a-117*A,609/2*a+241/2*A,161*a+72*A, 231/2*a+50*A,-120*a-44*A,252*a+76*A,-34*a-17/2*A,-19/2*a+A,-75/2*a-12*A, 189/2*a+24*A,-159*a-71*A,-143/2*a-21/2*A,125/2*a+51/2*A,216*a+125/2*A, 237/2*a+41/2*A,274*a+249/2*A,421/2*a+76*A,27/2*a-3*A,9*A,-183/2*a-22*A, 172*a+69*A,-2*a+3/2*A,15*a+12*A,429/2*a+173/2*A,159/2*a+25*A,4*a+33/2*A, -78*a-36*A,389/2*a+73*A,239/2*a+51*A,145/2*a+29*A,-73*a-67/2*A,-121/2*a-27*A, -223/2*a-59/2*A,393/2*a+72*A,5/2*a-11/2*A,315*a+107*A,171*a+54*A, -405/2*a-179/2*A,-515/2*a-219/2*A]]]; return result;