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

From Groupprops

## Statement

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

## Related facts

### Converse

### Similar facts

- Degrees of irreducible representations need not determine group up to isoclinism
- Degrees of irreducible representations need not determine nilpotency class
- Degrees of irreducible representations need not determine derived length

## Proof

The smallest example orders are:

- Order
- Order
- Order