JOURNAL OF SYMBOLIC COMPUTATION, vol.114, pp.267-281, 2023 (SCI-Expanded)
The category XSq of crossed squares is equivalent to the category Cat2 of cat(2)-groups. Functions for computing with these structures have been developed in the package XMod written using the GAP computational discrete algebra programming language. This paper contains a table listing the numbers iota(2)(G)& nbsp;of isomorphism classes of cat(2)-groups on groups G of order at most 30 - a total of 1007 cat(2)- groups. Secondly, it contains general formulae for iota(2)(G) in a number of special cases. (C)& nbsp;2022 Elsevier Ltd. All rights reserved.