Short character values on large conjugacy classes

TL;DR

This paper presents an example of a finite group with a large conjugacy class where less than half of the irreducible characters are either zero or roots of unity, challenging previous assumptions.

Contribution

It provides a specific example illustrating unusual character value behavior on large conjugacy classes in finite groups.

Findings

Existence of a finite group with a large conjugacy class and atypical character values

Less than half of the irreducible characters are zero or roots of unity on this class

Challenges existing beliefs about character values on large conjugacy classes

Abstract

We provide an example of a finite group with a conjugacy class of average size on which fewer than half of the irreducible characters are either zero or a root of unity.