Character of induced representation is induced class function of character

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Statement

Suppose H is a subgroup of finite index in a group G. Suppose \varphi is a finite-dimensional linear representation of H. Let \chi be the character of \varphi. Then, we have:

character of the induced representation \operatorname{Ind}_H^G(\varphi) = induced class function \operatorname{Ind}_H^G \chi