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!