Projective normality of finite group quotients

In this paper, we prove that for any finite dimensional vector space $V$ over an algebraically closed field $k$, and for any finite subgroup $G$ of $GL(V)$ which is either solvable or is generated by pseudo reflections such that $\vert G\vert$ is a unit in $k$, the projective variety $\mathbb{P}(V)/G$ is projectively normal with respect to the descent of $\mathcal O(1)^{\otimes \vert G\vert}$.