Computing 3-Dimensional Groups: Crossed Squares and Cat2-Groups

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 ι G 2 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 ι G 2 in a number of special cases.