Let $G$ the group of affine trasformations of $\mathbb{R}^n$. If $G_0$ is a closed subgroup of $GL(n, \mathbb{R}) $ , we can see $G$ as $G_0 \times \mathbb{R}^n$. In fact if $\phi_{g,v}(x) \in G$, then $\phi_{g,v}(x)= gx + v$ with $g \in G_0$ and $v \in \mathbb{R}^n$. Let $H= \{e\} \times \mathbb{R}^n$, where $e$ is the identity in $G_0$. I know that $H \subseteq G$ is a subgroup normal.$\\$ I can't prove that $G/H$ is unimodular. Then I should prove, using the fact that $G/H$ is unimodular, that the modular function of the group $G$ is $ \Delta_G= |det\ g|^{-1}$.
How can I prove that $G/H$ is unimodular?