# Is there a connected compact manifold $M$ of dimension 4 such that $\pi_1 (M) = \mathbb{Z} * (\mathbb{Z} \oplus \mathbb{Z}_3)$?

Is there a connected compact manifold $M$ of dimension 4 such that $\pi_1 (M) = \mathbb{Z} * (\mathbb{Z} \oplus \mathbb{Z}_3)$? I had this question in a test yesterday. I think that the answer is no, because of the $\mathbb{Z}_3$ (it in general makes things not locally euclidean), however I do not know how to prove it.