[GAP Forum] Programming

[Adnan Hamid]

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,