Suppose G_i$G_i$ are finite groups for i=1,2$i=1,2$ and G is the direct product of G_i$G_i$. If V is a finite dimensional irreducible representation of G$G$, then it is well known that V$V$ is a tensor product of V_i,i=1$V_i$,2$i=1,2$ and each V_i$V_i$ is an irreducible representation of G_i$G_i$.
The question I have is when V$V$ is given, is there a canonical way to construct V_i$V_i$ from V$V$?
