Class 2 quotients of solvable linear groups

Let $G$ be a finite group, and let $V$ be a completely reducible faithful $G$-module. By a result of Glauberman it has been known for a long time that if $G$ is nilpotent of class 2, then $\mathrm{\mid }G\mathrm{\mid }<\mathrm{\mid }V\mathrm{\mid }$. In this paper we generalize this result as follows. Assuming $G$ to be solvable, we show that the order of the maximal class 2 quotient of $G$ is strictly bounded above by $\mathrm{\mid }V\mathrm{\mid }$.