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It makes sense for me to show you what code I thought would work maybe you can tell me what I am doing wrong. After implementing the code you gave me above, I used the following: xy=G(x)*G(y) P = G.subgroup([xy]) G.cosets(P, side='left')

Thank you for taking a look at this...I do see that the group is isomorphic to A5, but I was hoping that sage could actually give me a list of representatives from the 12 cosets generated by xy. What I mean is...is there a way to give me the list: x<xy>, y<xy>, yx^2y<xy>, and so on?

I have created the following group:

sage: F.<x,y> = FreeGroup()
sage: G = F / [x^3, y^2, (x*y)^5]
sage: G
Finitely presented group < x, y | x^3, y^2, (x*y)^5 >

I would like to list the distinct cosets generated by <x*y>. I think there should be 12, but I have tried different code with no luck.