class equation theorem

Let $G$ be a group acting on a finite set $X$. Define the set of invariants in $X$ by the action of $G$ as $G_X=\{x\in X\mathit{\hspace{1em}}|\mathit{\hspace{1em}}gx=x\mathit{\hspace{1em}}\forall g\in G\}$. Then there are $H_1,\mathrm{\dots },H_r$ subgroups of $G$ with $H_i\ne G\mathit{\hspace{1em}}\forall i$ such that$\mathrm{\#}X=\mathrm{\#}{G}_X+{\sum }_{i=1}^r[G:H_i]$