It is well known that given a finite group $G$ and an irreducible representation $(V,\rho)$, we have a projector $$e_V=\frac{\chi(1)}{|G|}\sum_{g\in G}\chi(g^{-1})g\in\mathbb{C}G,$$ such that $e_V^2=e_V$ and gives the projection $\pi:\mathbb{C}G\to V^{\oplus\dim V}$, $x\mapsto xe_V$.
But how can I find a projector onto a single copy of $V$, i.e. $\pi:\mathbb{C}G\to V$? (In this case, there should be at least $(\dim V)$ of such projectors.)
If a general solution does not exist, how can I deal with a particular case? Especially I need to find it for $G=A_4$ and $V$ is the unique three dimensional irreducible representation.