If $G$ is a connected  Lie group  acting on a vector $\mathbb{C}$-space $V$  then it is well known that the algebra of invariants  $\mathbb{C}[V]^G$ coincides with  the algebra of invariants $\mathbb{C}[V]^L$ of  corresponding Lie algebra $L.$

**Question.** Let now $G$ be a finite group, $V$ be its representation and $\mathbb{C}[V]^G$. Is there existі a Lie algebra $L$ and its representation on $V$ such that $\mathbb{C}[V]^G=\mathbb{C}[V]^L$?

It is easy to see  that it impossible  for symmetric group $S_n$. But maybe there are classes of finite groups for which can be found the positive answer?