Character table sudokus

TL;DR

This paper explores the reconstruction of missing parts in character tables of finite groups, utilizing properties of ramified characters, and extends classifications of groups with large character degrees.

Contribution

It introduces methods to reconstruct missing rows or columns in character tables and extends existing classifications of groups with large character degrees.

Findings

Reconstruction of missing table parts is possible using ramified character properties.

Extended classification of groups with large character degrees.

Deep properties of characters underpin the reconstruction methods.

Abstract

It is a fun game to complete a partial character table of a finite group. We show that one can reconstruct a missing row or column from a given table. The proof relies on deep properties of fully ramified characters. Moreover, we extend a classification of groups with a "large" character degree started by Snyder and continued by Durfee and Jensen.