An Algorithm for Constructing All Supercharacter Theories of a Finite Group

TL;DR

This paper presents an algorithm to systematically construct all supercharacter theories of finite groups, enabling comprehensive analysis of their structure, especially for groups with up to 14 conjugacy classes.

Contribution

The paper introduces a novel algorithm that efficiently generates all supercharacter theories for finite groups, expanding the computational tools available in this area.

Findings

Successfully computed all supercharacter theories for groups with up to 14 conjugacy classes.

Provides a practical method for exploring supercharacter theories in finite group analysis.

Enhances understanding of the structure and classification of supercharacter theories.

Abstract

In 2008, Diaconis annd Isaacs introduced the notion of a supercharacter theory of a finite group in which supercharacters replace with irreducible characters and superclasses by conjugacy classes. In this paper, we introduce an algorithm for constructing supercharacter theories of a finite group by which all supercharacter theories of groups containing up to 14 conjugacy classes are calculated.