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.

Related facts

 * Induced representation from trivial representation on normal subgroup factors through regular representation of quotient group
 * Induced representation from regular representation of subgroup is regular representation of group