Character of induced representation is induced class function of character

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 $$\operatorname{Ind}_H^G \chi$$