An algorithm for computing Schur indices of characters

TL;DR

This paper presents an algorithm for calculating Schur indices of irreducible characters of finite groups, implemented in Magma, with comparisons to known results for sporadic simple groups.

Contribution

It introduces a new algorithm for computing Schur indices based on subgroup character table computations, implemented in Magma.

Findings

Algorithm successfully computes Schur indices for various groups.

Comparison with Feit's results highlights differences in certain cases.

Implementation demonstrates practical utility for complex group analysis.

Abstract

We describe an algorithm for computing Schur indices of irreducible characters of a finite group $G$, based on computations within $G$ and its subgroups and with their character tables. The algorithm has been implemented within \Magma\ and examples of its use are given. We also compare the output of the algorithm on groups associated with sporadic simple groups with the results of W. Feit. The differences are considered.