# Conjugacy class size statistics need not determine degrees of irreducible representations

## Statement

It is possible to have two finite groups $G_1$ and $G_2$ such that the conjugacy class size statistics of $G_1$ are the same as those of $G_2$ (i.e., the two groups have the same number of conjugacy classes of each size) but the Degrees of irreducible representations (?) over $\mathbb{C}$ for $G_1$ are not the same as those of $G_2$.

## Proof

The smallest examples are among groups of order 128.