  Let G be a linear group acting on the finite vector space V and assume that
(|G|,|V|)=1. In this paper we prove that G has a base size at most two and this
estimate is sharp. This generalizes and strengthens several former results
concerning base sizes of coprime linear groups. As a direct consequence, we
answer a question of I. M. Isaacs in the affirmative. Via large orbits this is
related to the k(GV) theorem.
