# Degrees of irreducible representations need not determine conjugacy class size statistics

## Statement

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

## Proof

The smallest example orders are:

• Order $64 = 2^6$
• Order $96 = 2^5 \cdot 3$
• Order $243 = 3^5$