ENUMERATION OF CAT¹-GROUPS OF LOW ORDER

In this paper we describe a share package of functions for computing with finite, permutation crossed modules, cat¹-groups and their morphisms, written using the group theory programming language. The category XMod of crossed modules is equivalent to the category Cat1 of cat¹-groups and we include functions emulating the functors between these categories. The monoid of derivations of a crossed module , and the corresponding monoid of sections of a cat¹-group , are constructed using the Whitehead multiplication. The Whitehead group of invertible derivations, together with the group of automorphisms of , are used to construct the actor crossed module of which is the automorphism object in XMod. We include a table of the 350 isomorphism classes of cat¹-structures on groups of order at most 30.