Equivariant unirationality of del Pezzo surfaces of degree 3 and 4

A variety X with an action of a finite group G is said to be G-unirational if there is a G-equivariant dominant rational map V --> X where V is a faithful linear representation of G. This generalizes the usual notion of unirationality. We determine when X is G-unirational for any complex del Pezzo surface X of degree at least 3.