Open main menu

Groupprops β

Conjugacy class size statistics of a finite group

Contents

Definition

Let G be a finite group. The conjugacy class size statistics of G is a function f:\mathbb{N} \to \mathbb{N}_0 that outputs, for each d, the number of conjugacy classes of G of size d. Note that since size of conjugacy class divides order of group, the function is nonzero only on (some) divisors of the order of G.

The conjugacy class size statistics carry more information than the conjugacy class size set of a finite group, which is simply the set of sizes of the conjugacy classes in G.

Relation with other statistics

Facts