Sorry for all the recent posts, I don't want to throw all my homework questions into one big post, so instead I'm breaking them down. If this bothers anyone let me know though.
Anyways, another problem was to find the conjugacy classes of the infinite dihedral group. For those who need memory refreshing, the infinite dihedral group is: with e being the identity element.
I arrived at these three conjugacy classes:
Is there anything I missed? And if I did miss it, can you give me a hint as to how you found it?