  Let $G$ be a finite group, and let $V$ be a completely reducible faithful
$G$-module. It has been known for a long time that if $G$ is abelian, then $G$
has a regular orbit on $V$. In this paper we show that $G$ has an orbit of size
at least $|G/G'|$ on $V$. This generalizes earlier work of the authors, where
the same bound was proved under the additional hypothesis that $G$ is solvable.
For completely reducible modules it also strengthens the 1989 result
$|G/G'|<|V|$ by Aschbacher and Guralnick.
