Split extension of linear algebraic groups given by unipotent radicals and reductive groups

Question

I've read that there is a split extension of any linear algebraic group $G$ over a perfect field given by $$ 1 \to R_u(G) \to G \to H \to 1$$ where $R_u(G)$ is the radical unipotent subgroup of $G$ and $H$ is a reductive group, but I can't figure out what the section map is, explicitly.

So

In the above split sequence, what does the section $H \to G$ do, exactly?