2013-10-24 22:40:09 +0200 commented answer Cosets Generated by Product of Generators 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') 2013-10-24 22:07:23 +0200 commented answer Cosets Generated by Product of Generators 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, y, yx^2y, and so on? 2013-10-22 22:42:04 +0200 asked a question Cosets Generated by Product of Generators I have created the following group: sage: F. = 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 . I think there should be 12, but I have tried different code with no luck.