# Conjugacy class size statistics of a finite group

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

## 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 $G$.

## Facts

### Facts about conjugacy class sizes

Divisibility facts:

Bounding facts:

Non-divisibility/non-bounding facts:

### Relation with degrees of irreducible representations

The number of conjugacy classes is an important measure in relating conjugacy classes to irreducible representations and to the degrees of irreducible representations.