GAP computations needed in the proof of [DNT, Theorem 6.1 (ii)]

TL;DR

This paper provides example computations demonstrating that certain group extensions do not have all complex irreducible characters of the same degree Galois conjugate, supporting a key theorem in group theory.

Contribution

It supplies explicit GAP computations needed to verify a specific property in the proof of a major theorem in finite group theory.

Findings

Extension of finite simple groups by elementary abelian groups often have non-Galois conjugate characters.

Explicit GAP computations confirm the non-Galois conjugacy in specific cases.

Supports the proof of Theorem 6.1 (ii) in [DNT].

Abstract

This is a collection of example computations that are cited in the Appendix of [DNT]. In each case, the aim is to show that the extension of a given finite simple group by an elementary abelian group of given rank has the property that not all complex irreducible characters of the same degree are Galois conjugate.