Is this claim right or is there a counter example?

Question

Now let $G$ be a finite topological group. Assume that $H$ is a subgroup of $G$. Then let $(\sigma,V_\sigma)$ be an irreducible representation of $H$. Let $Ind_H^G(\sigma)$ be the induced representation on $G$. More explicitly, the definition here is as below: My question is the claim below $$ \mathbb{C}G\otimes_{\mathbb{C}H}V_\sigma\cong Ind_H^G(\sigma) $$ How can I find an access to the proof?Looking forward to the sincere help.