\begin{definition}[Definition:Permutation Representation]
Let $G$ be a group.
Let $X$ be a set.
Let $\struct {\map \Gamma X, \circ}$ be the symmetric group on $X$.
A '''permutation representation''' of $G$ is a group homomorphism from $G$ to $\struct {\map \Gamma X, \circ}$.
\end{definition}