TITLE: Examples of $X$ such that $\pi_1(X) $ not abelian?
QUESTION [6 upvotes]: I've come up with some examples to apply the Hurewicz theorem to compute $H_1(X)$.
This is only interesting if $\pi_1(X)$ is not abelian. The only examples of $X$ such that $\pi_1(X)$ not abelian I can come up with are $\vee_i S^1$ and $\Sigma_g$ the surface of genus $g$ for $g > 1$.
Does anyone know any other examples, preferably easy ones? Many thanks for your help!

REPLY [6 votes]: One more example: complement to any non-trivial knot in $S^3$ has non-abelian $\pi_1$.