I have the group presentations

and

and am told to say what well-known groups they define. I know the second is the infinite dihedral group and so am guessing the first is , but don't know how to showwhythey are these groups.

Thanks

P.S. in an unrelated question, given a non-abelian group of order 60, how could you show that it has no odd permutations (without using the fact that it is )?