Induced representation from trivial representation of subgroup is permutation representation for action on coset space

Statement

Suppose $H$ is a normal subgroup of a group $G$ . Denote by $\psi$ the trivial representation of $H$ . Then, the induced representation $\operatorname{Ind}_H^G \psi$ can be viewed as a permutation representation. Specifically, the permutation representation is the group action on the left coset space $G/H$ by left multiplication.