The Automorphism Groups of the Groups of Order 8p^2

TL;DR

This paper computes the automorphism groups of all groups of order 8p and 8p^2, providing explicit presentations and using CAYLEY for calculations, advancing understanding of their symmetries.

Contribution

It offers the first comprehensive determination of automorphism groups for these specific classes of groups, including explicit presentations and computational methods.

Findings

Automorphism groups for groups of order 8p and 8p^2 are explicitly determined.

Calculations were performed using the CAYLEY programming language.

Explicit presentations of the groups and their automorphism groups are provided.

Abstract

The automorphism groups for the groups of orders $8p$ and $8p^2$ are given. The calculations were done using the programming language CAYLEY. Explicit presentations for both the groups of these orders and their automorphism groups are given.