# Finite group having the same orbit sizes of conjugacy classes and irreducible representations under automorphism group

From Groupprops

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## Definition

A finite group is said to have the **same orbit sizes of conjugacy classes and irreducible representations under automorphism group** if the following holds:

Let be the set of conjugacy classes of and be the set of irreducible representations (up to equivalence) of over . The automorphism group acts on both and . The condition we need is that the orbit sizes in and be equal.