I have to prove that a group G of order 64 cannot have a trivial center.
In the case that G is Abelian, this is trivial, as the center of Abelian group is the group itself.
What to do in the case that G is non-Abelian?
I've found this Center of Group of Prime Power Order is Non-Trivial, - ProofWiki but the proof uses many things we have not discussed in class so there has to be another way.
Thanks for all your help!