Definition:Permutation Representation

Definition
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 $\struct {\map \Gamma X, \circ}$.

Also see

 * Correspondence Between Group Actions and Permutation Representations