A result closely related to the orbit-stabilizer theorem is Burnside's lemma : | X / G | = 1 | G | ∑ ∑ g ∈ ∈ G | X g | , where X is the set of points fixed by g. This result is mainly of use when G and X are finite, when it can be interpreted as follows: the number of orbits is equal to the average number of points fixed per group element.