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 $G$.

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• Frobenius reciprocity