Group homomorphism/To permutation group/On power set/Exercise

Let ${}G$ be a group, let ${}M$ denote a set, and let

$G\longrightarrow \operatorname {Perm} \,(M),g\longmapsto \sigma _{g},$

denote a group homomorphism into the permutation group of ${}M$. Show that this induces in a natural way a group homomorphism

$G\longrightarrow \operatorname {Perm({\mathfrak {P}}\,(M))} \,,g\longmapsto (N\mapsto g(N)),$

in the permutation group of the power set.

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