Enumeration of Cat1-Groups of Low Order

In this paper we describe a share package $\mathsf {XMOD}$ of functions for computing with finite, permutation crossed modules, cat1-groups and their morphisms, written using the $\mathsf {GAP}$ 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 ${\mathcal X}$ , and the corresponding monoid of sections of a cat1-group ${\mathcal C}$ , are constructed using the Whitehead multiplication. The Whitehead group of invertible derivations, together with the group of automorphisms of ${\mathcal X}$ , are used to construct the actor crossed module of ${\mathcal X}$ 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.