The groups of order 256
type: Item
instance of: scholarly article
title: The groups of order 256
zbMATH Open document ID: 0734.20001
DOI: 10.1016/0021-8693(91)90261-6
author: E. A. O'Brien
published in: Journal of Algebra
publication date: 1991-01-01T00:00:00Z
review text: The algorithm that has been used by the author for the complete classification of all (56092) groups of order 256 (up to isomorphism) was proposed by \textit{M. F. Newman} [Lect. Notes Math. 573, 73-84 (1977; Zbl 0519.20018)]. The author has described this algorithm and an implementation in detail in a previous paper [J. Symb. Comput. 9, 677-698 (1990; Zbl 0736.20001)]. This paper gives details of an extension of the algorithm that was necessary in order to be able also to classify the 5- and 6-generator groups among the groups of order 256 and gives a summary of the results of the computation. The complete list of these groups is available with the computational group theory systems CAYLEY and GAP in a form that allows further work with these groups using these computational group theory systems.
Mathematics Subject Classification ID: 20-04
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20F14
Mathematics Subject Classification ID: 20F18
zbMATH DE Number: 4214237
zbMATH Keywords: p-group generation
zbMATH Keywords: nilpotient quotient algorithm
zbMATH Keywords: 5- and 6-generator groups
zbMATH Keywords: groups of order 256
zbMATH Keywords: CAYLEY
zbMATH Keywords: GAP
zbMATH Keywords: computational group theory
reviewed by: Joachim Neubüser
describes a project that uses: Cayley
describes a project that uses: GAP
MaRDI profile type: Publication
full work available at URL: 0021-8693(91)90261-6
OpenAlex ID: W2040685037
cites work: Q3333220
cites work: Q5840123
cites work: Enumerating p -Groups. I: Inequalities
cites work: The groups of order 128
cites work: Q3669627
cites work: Q3810818
cites work: The \(p\)-group generation algorithm
description: scientific article; zbMATH DE number 4214237