A supercharacter theory for Sylow $p$-subgroups of the Steinberg triality groups

TL;DR

This paper develops a supercharacter theory for the Sylow p-subgroup of the Steinberg triality group ${^3}D_4(q^3)$, providing a detailed supercharacter table and advancing understanding of its algebraic structure.

Contribution

It introduces a novel supercharacter theory specifically for the Sylow p-subgroup of ${^3}D_4(q^3)$, expanding the toolkit for analyzing these groups.

Findings

Constructed the supercharacter theory for ${^3}D_4^{syl}(q^3)$

Established the supercharacter table for the subgroup

Enhanced understanding of the group's algebraic properties

Abstract

We determine a supercharacter theory for the matrix Sylow $p$-subgroup ${^3}D_4^{syl}(q^3)$ of the Steinberg triality group ${^3}D_4(q^3)$, and establish the supercharacter table of ${^3}D_4^{syl}(q^3)$.