# Character: X6 # Comment: perm rep on 406 pts (cosets of D30) # Ind: 1 # Ring: C # Sparsity: 85% # 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 := "L229 as 28 x 28 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], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [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], [3621/341*a+1528/341*A,3425/341*a+1109/341*A,3253/341*a+1305/341*A, 4014/341*a+1326/341*A,2135/341*a+874/341*A,3842/341*a+1522/341*A, 2135/341*a+874/341*A,1373/341*a+529/341*A,3402/341*a+1159/341*A, 444/341*a+295/341*A,1373/341*a+529/341*A,3402/341*a+1159/341*A,4255/341*a+1321/341*A, 444/341*a+295/341*A,235/341*a+438/341*A,37/31*a+22/31*A,1238/341*a+778/341*A, 860/341*a+384/341*A,235/341*a+438/341*A,37/31*a+22/31*A,1410/341*a+582/341*A, 1645/341*a+679/341*A,860/341*a+384/341*A,-1,0,-172/341*a+196/341*A, 172/341*a-196/341*A,1645/341*a+679/341*A], [2488/341*a+1011/341*A,2677/341*a+1208/341*A,1966/341*a+678/341*A, 2925/341*a+1084/341*A,1607/341*a+643/341*A,2214/341*a+554/341*A, 1607/341*a+643/341*A,856/341*a+111/341*A,2346/341*a+697/341*A,400/341*a+361/341*A, 856/341*a+111/341*A,2346/341*a+697/341*A,2924/341*a+760/341*A,400/341*a+361/341*A, -117/341*a-57/341*A,54/31*a+12/31*A,633/341*a+151/341*A,827/341*a+263/341*A, -117/341*a-57/341*A,54/31*a+12/31*A,1344/341*a+681/341*A,886/341*a+283/341*A, 827/341*a+263/341*A,0,-1,-711/341*a-530/341*A,711/341*a+530/341*A, 886/341*a+283/341*A], [-1,-1,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,-1,0], [-1,0,-1,0,0,-1,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,-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]] , [[0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,-1,0,0,-1,0,-1,0,-1,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [3819/341*a+1231/341*A,4294/341*a+3045/341*A,3319/341*a+524/341*A, 4542/341*a+1898/341*A,2608/341*a+1699/341*A,3908/341*a+741/341*A, 1926/341*a-6/341*A,1417/341*a+122/341*A,3666/341*a+1104/341*A,455/341*a+108/341*A, 1076/341*a-560/341*A,3666/341*a+1104/341*A,4673/341*a+1376/341*A, 796/341*a+1131/341*A,-18/341*a-35/341*A,-37/31*a-208/31*A,963/341*a-344/341*A, 1124/341*a+1011/341*A,-700/341*a-2081/341*A,87/31*a+133/31*A,1597/341*a+813/341*A, 1238/341*a-586/341*A,442/341*a-1035/341*A,-3*A,2*a+5*A,-975/341*a-1839/341*A, 975/341*a+1839/341*A,1920/341*a+1119/341*A], [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], [-4261/341*a-1901/341*A,-3902/341*a-1525/341*A,-3921/341*a-1543/341*A, -4739/341*a-1959/341*A,-2169/341*a-637/341*A,-4758/341*a-1977/341*A, -2510/341*a-978/341*A,-1591/341*a-574/341*A,-4307/341*a-1801/341*A, -514/341*a-128/341*A,-1591/341*a-574/341*A,-3966/341*a-1460/341*A, -5210/341*a-2136/341*A,-514/341*a-128/341*A,-206/341*a+92/341*A, -48/31*a-52/31*A,-1255/341*a-489/341*A,-587/341*a+90/341*A,-206/341*a-249/341*A, 14/31*a+41/31*A,-1577/341*a-812/341*A,-2124/341*a-1061/341*A,-928/341*a-592/341*A, -2*a-A,-1,322/341*a-18/341*A,19/341*a+18/341*A,-1783/341*a-379/341*A ], [-342/341*a+17/341*A,-695/341*a-1143/341*A,-114/341*a+574/341*A,-478/341*a-399/341*A, -259/341*a-371/341*A,-579/341*a-46/341*A,82/341*a+652/341*A,-76/341*a+269/341*A, -425/341*a-277/341*A,-112/341*a+199/341*A,265/341*a+610/341*A,-84/341*a+405/341*A, -505/341*a-281/341*A,-112/341*a-483/341*A,-90/341*a+166/341*A,63/31*a+138/31*A, 41/341*a+667/341*A,-177/341*a-401/341*A,592/341*a+1530/341*A,1/31*a-48/31*A, 142/341*a-27/341*A,52/341*a+821/341*A,505/341*a+963/341*A,2*A,-2*A, 240/341*a+1035/341*A,-240/341*a-1035/341*A,-289/341*a-202/341*A], [-1,-1,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,-1,0], [-5*a-2*A,-4*a,-6*a-3*A,-6*a-2*A,-2*a,-6*a-3*A,-4*a-2*A,-2*a-A,-5*a-2*A, 0,-3*a-2*A,-6*a-3*A,-7*a-3*A,A,0,-a-2*A,1,-a,-a-2*A,A,-2*a,-3*a-2*A, 2,1,a+2*A,-A,a+2*A,-3*a-A]]]; return result;