Exercise 19, § 2

Let $G$ be a finite group and $H$ a subgroup of $G$. For every unitary representation $\pi$ of $H$ in a finite-dimensional complex Hilbert space E, prove that the induced unitary representation Ind$^G_H(\pi )$ is isomorphic to the induced representation defined in A, VIII, p. 392, § 21, No. 3.