My notes ask me to confirm the result:
$\mathrm{Hom}(V \otimes W, U) \cong \mathrm{Hom}(V, \mathrm{Hom}(U,W))$ as $\mathbb C$-representations of a finite group $G$.
But it seems to be incorrect. $\chi_{\mathrm{Hom}(V \otimes W, U)} = \overline{\chi_{V \otimes W}} \chi_U = \overline{\chi_V}\ \overline{\chi _ W} \chi_U$, whilst $\chi_{\mathrm{Hom}(V, \mathrm{Hom}(U,W))} = \overline{\chi_V} \chi_{\mathrm{Hom}(U,W)} = \overline{\chi_V} \ \overline{\chi_U} \chi_W$. So it looks like $U$ and $W$ should be switched in the RHS of the isomorphism.
Am I right?
Thanks