Lattices in ${\mathbb{R}}^n⋊{\text{SL}}_2(\mathbb{R})$

We determine the existence of cocompact lattices in groups of the form $\text{V}⋊{\text{SL}}_2(\mathbb{R})$, where $\text{V}$ is a finite dimensional real representation of ${\text{SL}}_2(\mathbb{R})$. It turns out that the answer depends on the parity of $\dim (\text{V})$ when the representation is irreducible.