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

From Groupprops

## Statement

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

## Related facts

### Converse

### Similar facts

- Conjugacy class size statistics need not determine group up to isoclinism
- Conjugacy class size statistics need not determine nilpotency class
- Conjugacy class size statistics need not determine derived length

## Proof

`Further information: Linear representation theory of groups of order 128#Degrees of irreducible representations, element structure of groups of order 128#Conjugacy class sizes`

The smallest examples are among groups of order 128.