Consider $M = H_{\mathbb{R}}/H_{\mathbb{Z}}$, where $H_{\mathbb{R}} = \lbrace\begin{bmatrix} 1 & x & z \\ 0 & 1 & y \\ 0 & 0 & 1\\ \end{bmatrix}|x,y,z \in \mathbb{R}\rbrace$ and $H_{\mathbb{Z}} = \lbrace\begin{bmatrix} 1 & x & z \\ 0 & 1 & y \\ 0 & 0 & 1\\ \end{bmatrix}|x,y,z \in \mathbb{Z}\rbrace$
If we regards $M$ as a manifold (Only need to consider $M$ as topological manifold).
What is the fundamental group of $M$, $\pi_1(M)$? How to deduce that?
Thank you very much!