Character tables of Sylow $p$-subgroups of the Steinberg triality groups ${^3}D_4(q^3)$

TL;DR

This paper computes the character tables of Sylow p-subgroups of the Steinberg triality groups ${^3}D_4(q^3)$, providing detailed representation-theoretic data for these algebraic groups.

Contribution

It explicitly determines the character tables of Sylow p-subgroups of the Steinberg triality groups ${^3}D_4(q^3)$, a previously uncharted area in group representation theory.

Findings

Complete character tables for Sylow p-subgroups of ${^3}D_4(q^3)$

New insights into the structure of these subgroups

Foundation for further representation-theoretic studies

Abstract

We determine the character tables of Sylow $p$-subgroups $U$ of the Steinberg triality groups ${^3}D_4(q^3)$, where $q$ is a power of an odd prime $p$.