I am working on a problem saying that:
If $$D_{2n}=\left\{\begin{pmatrix}\epsilon & k \\ 0 & 1\end{pmatrix}|\epsilon=±1,k\in\mathbb Z_n \right \}$$ then for any $n\in\mathbb N$, $D_{2n}$ is a quotient group of $$D_\infty=\left\{\begin{pmatrix}\epsilon & k \\ 0 & 1\end{pmatrix}|\epsilon=±1,k\in\mathbb Z \right \}$$ May I ask if this later group is infinite dihedral group as we have already known? May I ask how it can be? Thanks.