Supercharacter theories for Sylow $p$-subgroups of the Ree groups

TL;DR

This paper develops a supercharacter theory for Sylow p-subgroups of Ree groups, explicitly determining conjugacy classes and character tables, thereby advancing understanding of their representation structure.

Contribution

It introduces a new supercharacter theory for Sylow p-subgroups of Ree groups and computes their conjugacy classes and character table.

Findings

Supercharacter theory for Sylow p-subgroups of Ree groups established

Conjugacy classes explicitly calculated

Character table of the specific Sylow subgroup determined

Abstract

We determine a supercharacter theory for Sylow $p$-subgroups ${^2{G}_2^{syl}(3^{2m+1})}$ of the Ree groups $^2{G}_2(3^{2m+1})$, calculate the conjugacy classes of ${^2{G}_2^{syl}(3^{2m+1})}$, and establish the character table of ${^2{G}_2^{syl}(3)}$.