Degree of induced representation from subgroup is product of degree of original representation and index of subgroup

Statement

Suppose $G$ is a group, $H$ is a subgroup of $G$ , and $\varphi$ is a linear representation of $H$ over a field $K$ . Denote by $\operatorname{Ind}_H^G\varphi$ the induced representation of $\varphi$ from $H$ to $G$ . Then, the degree of $\operatorname{Ind}_H^G\varphi$ is the product of the degree of $\varphi$ and the index of $H$ in $G$ .