The Character Table of $\text{GL}_n(\mathbb{F}_q)\rtimes\!<\!\sigma\!>\!$

TL;DR

This paper computes the character table of a semidirect product involving the general linear group over a finite field and an order 2 automorphism, providing detailed representation-theoretic data.

Contribution

It explicitly determines the character table of the group ext{GL}_n( ext{F}_q) times ext{<}\sigma ext{>}, where \sigma is an order 2 automorphism, a task not previously completed.

Findings

Explicit character table for ext{GL}_n( ext{F}_q) times ext{<}\sigma ext{>}

New insights into automorphism-induced group extensions

Enhanced understanding of representations of finite groups with automorphisms

Abstract

We compute the character table of $\text{GL}_n(\mathbb{F}_q)\rtimes\!<\!\sigma\!>\!$, $\sigma$ being an order 2 exterior automorphism.