Let $G$ be a [simple group](/page/Simple%20Group) with identity element $e_G$, let $X$ be a set, and let $G$ act on $X$. Let $S_X$ denote the [symmetric group](/page/Symmetric%20Group) of all bijections $X \to X$, with identity element $\operatorname{id}_X$, and let $\varphi: G \to S_X$ be the associated permutation representation of the action. Then either $\varphi(G)=\{\operatorname{id}_X\}$, or the action is faithful.