Let G be group of order 54
a. If G is abelian, what groups can it be up to isomorphisms
b. If G is nonabelian and the order of G is 24 and G is isomorphic to H x Z_3, what are the possibilities for H up to isomorphism
c. If p and q are distinct primes, how many abelian groups are there of order p (square) q(fourth)?
This solution demonstrates how to solve the given problems regarding abelian groups.