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In this note, we prove:  \medskip \noindent {\bf Theorem A:} \emph{ There is a fixed constant $C$ suchthat for any positive integer $n$ and prime $p$, every finite subgroup $G$ oforder coprime to $p$ of ${\rm GL}(n,\mathbb{C})$ has an Abelian normal subgroup$A$ with $$[G:A] \leq (Cp)^{n-1}.$$}

Bounding the order of finite $p^{\prime}$- subgroups of ${\rm GL}(n,\mathbb{C})$