Presentation of 2-Group of Order 32

Abstract

Research on the presentation of 2-groups of order $2^n,$ $(n\le 6)$ was founded by Hall et al. [4] and was continued by Sag et al [7]. This paper focuses on the presentation of 2-groups of order $2^5$ where there are 51 groups comprising of 7 Abelian groups and 44 non-Abelian groups. We are more concerned in finding the structures for each of the every 44 non-Abelian groups to show that these groups are not isomorphic to each other using GAP (Groups, Algorithms, and Programming) software. Keywords: 2-Group; group presentation; isomorphism; non-Abelian group.