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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