Dear Programmer; Suppose that G=PSL(2,11), c = (1, 2)(3 ,4)(5, 12)(6 ,11)(7, 10)(8 ,9) in G , D10∼=DihedralGroup( 10 ), Since G has one conjugacy class of subgroups isomorphic to DihedralGroup( 10 ), we may assume that D10 ∼= H. So, L ∼= Cos(G,H,HgH), where g ∈ G is a 2-element such that g^2 ∈ H, |HgH|/|H| = 5 and <H, g> = G. Set H g ∩ H = < x >. Since H∼=DihedralGroup( 10 ), x = c^y for some y ∈ H. Set d = g^y. Then d ∈ C(c) ∼= DihedralGroup( 24 ) and Cos(G,H,HgH) = Cos(G,H,HdH). Since <H, d> = G, g has six choices.(C(c) is centralizer c in G). How do I find choices of g? Best regards, _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
