# Character: X5 # Comment: perm rep on 285 pts # Ind: 1 # Ring: C # Sparsity: 76% # 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 := "L219 as 18 x 18 matrices\n"; result.generators := [ [[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], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0], [0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0], [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0], [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0], [921/541*a+481/541*A,287/541*a+154/541*A,1487/541*a+534/541*A,1527/541*a+727/541*A, 1667/541*a+591/541*A,1966/541*a+857/541*A,315/541*a+235/541*A,-196/541*a-567/541*A, 817/541*a+412/541*A,530/541*a+1340/541*A,-436/541*a-643/541*A,649/541*a-74/541*A, 1010/541*a+1492/541*A,256/541*a+586/541*A,941/541*a+307/541*A,924/541*a-32/541*A, 578/541*a+165/541*A,-206/541*a+61/541*A], [101/541*a+582/541*A,408/541*a+562/541*A,129/541*a+122/541*A,-259/541*a-73/541*A, 6/541*a+56/541*A,-27/541*a+289/541*A,461/541*a+155/541*A,-371/541*a-397/541*A, 677/541*a+548/541*A,269/541*a+527/541*A,-207/541*a-309/541*A,359/541*a+285/541*A, -59/541*a+351/541*A,330/541*a+375/541*A,-93/541*a+214/541*A,126/541*a+94/541*A, -413/541*a-248/541*A,267/541*a+328/541*A], [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0], [481/541*a+522/541*A,154/541*a+175/541*A,1075/541*a+1197/541*A,727/541*a+654/541*A, 1132/541*a+1188/541*A,857/541*a+605/541*A,235/541*a+390/541*A,515/541*a+659/541*A, 412/541*a+419/541*A,258/541*a+244/541*A,439/541*a+671/541*A,467/541*a+752/541*A, 410/541*a+220/541*A,45/541*a+420/541*A,307/541*a-20/541*A,509/541*a+603/541*A, 706/541*a+458/541*A,61/541*a+389/541*A], [-41/541*a-22/541*A,-21/541*a+345/541*A,-122/541*a+304/541*A,73/541*a-40/541*A, -56/541*a+379/541*A,252/541*a+188/541*A,-155/541*a-4/541*A,397/541*a+820/541*A, -7/541*a+115/541*A,-527/541*a-1312/541*A,309/541*a+720/541*A,256/541*a+586/541*A, -351/541*a-1112/541*A,-375/541*a-795/541*A,327/541*a+347/541*A,447/541*a+926/541*A, 248/541*a+331/541*A,213/541*a-176/541*A]] , [[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], [0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0], [0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], [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], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0], [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1], [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0], [1641/541*a+1250/541*A,603/541*a+759/541*A,2112/541*a+1859/541*A,1459/541*a+994/541*A, 2690/541*a+2024/541*A,1961/541*a+1171/541*A,200/541*a+424/541*A, 1198/541*a+1263/541*A,1283/541*a+794/541*A,-402/541*a-506/541*A, 247/541*a+502/541*A,996/541*a+1181/541*A,418/541*a-66/541*A,-284/541*a-126/541*A, 1044/541*a+547/541*A,1308/541*a+1388/541*A,1303/541*a+1161/541*A, 144/541*a+262/541*A], [-669/541*a-293/541*A,40/541*a+193/541*A,-1133/541*a-476/541*A,-1118/541*a-336/541*A, -1336/541*a-387/541*A,-1021/541*a-152/541*A,-220/541*a-250/541*A, -344/541*a-145/541*A,-708/541*a-116/541*A,334/541*a+232/541*A,107/541*a+97/541*A, -230/541*a-163/541*A,-568/541*a-252/541*A,96/541*a-186/541*A,-932/541*a-223/541*A, -1006/541*a-553/541*A,-730/541*a-141/541*A,58/541*a-180/541*A], [0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0], [-681/541*a+136/541*A,179/541*a+228/541*A,-918/541*a+88/541*A,-648/541*a-97/541*A, -785/541*a+67/541*A,-1066/541*a-31/541*A,-173/541*a+369/541*A,-241/541*a+95/541*A, -301/541*a+76/541*A,61/541*a+389/541*A,303/541*a+123/541*A,188/541*a+312/541*A, 55/541*a+333/541*A,105/541*a+439/541*A,-546/541*a-227/541*A,-796/541*a-216/541*A, -156/541*a+167/541*A,503/541*a+547/541*A]]]; return result;