Hi I'm looking for a way to represent groups in Maple.  I have looked at the groups package, and still don't know how to deal with cyclic groups, or how to deal with elements of a group.  Note, I think I know how to do these things for permutation groups but what if I want to do it with a different group, like Z3. I really appreciate any help you can give me, thank you.

I'm trying to write some mapplets for my professor (in Maple 11/12). Most importantly I need a program for working with group theory.  I've looked at the help menus in maple on the group package and all of its commands, I also read all of the maple programming booklets.  Still I have no idea how to do simple things like create the group Z₂ or S₃ and Z₂ + Z₂.  I anyone has any idea on where more information on these issues might be.