Solution
= Solution
For a finite <group> $G$ acting on a <set> $X$, write $G_x=\{g\in G:gx=x\}$ for the <stabilizer subgroup> and $Gx=\{gx:g\in G\}$ for the <orbit> of $x$. The <orbit-stabilizer theorem> gives
$$
\boxed{|G|=|G_x|\,|Gx|.}
$$
Indeed, $gG_x\mapsto gx$ is a <bijection> from the left <cosets> of $G_x$ onto $Gx$: two images agree precisely when $h^{-1}g\in G_x$. Each <coset> has $|G_x|$ elements, proving the formula.