Classify all groups of order 39
The Attempt at a Solution
I can show that if the group of abelian, it is isomorphic to Z/3Z*Z/13Z.
If the group is not abelian, there are two types of groups, they either follow the rule : x^3=e, y^13=e, and xy=y^3x; or x^3=e, y^13=e, and xy=y^9x. But I want to show that they are the same thing if I rename x^2=z.
But I want to prove that there is a homomorphic between these two groups. Could some one help me?