(;) Semicolon Math: Order of permutation

Let the set \(\{1,2,3, \ldots, n\}\) be denoted by \([n]\). A permutation of \([n]\) is a function \(f\) from \([n]\) to \([n]\) such that distinct elements of the domain map to distinct elements in the codomain, i.e. \(f(x) \neq f(y)\) if \(x \neq y\). Find the number of permutations \(\sigma(x)\) from \([6]\) to \([6]\) with \(\sigma^6 = e\), where \(e\) is the identity permutation defined by \(e(x) = x\) for all \(x\) in \([6]\). That is, applying the permutation six times results in the identity map.