# Definitions > [!NOTE] Definition (Orbit) > Let $G$ be a [[Finite Group|finite group]] [[Group action|acting]] on a finite set $X.$ The orbit of an element $x\in X$ is given by $O_{x}=\{ g *x \mid g\in G \}$where $*$ denotes the group action. # Properties The [[Orbit-Stabilizer Theorem]] asserts the existence of a bijection between the orbit of an element and the left coset space of the stabiliser of the element which means $|O_{x}|=|G|/|\text{Stab}_{G}(x)|.$