TITLE: Is there a non-abelian group of order 49?
QUESTION [5 upvotes]: Is there any non-abelian group of order $n=49$? I assume there should be at least one but I cannot find an example.

REPLY [5 votes]: The only groups of order $49$ are $\mathbb Z_{49}$ and $\mathbb Z_7\times \mathbb Z_7$ since $49$ is a square of a prime number.