Cat-1-groups

AutomorphismGroupAsCatOneGroup
AutomorphismGroupAsCatOneGroup(G)

Inputs a group G and returns the Cat-1-group C corresponding th the crossed module G\rightarrow Aut(G).
HomotopyGroup
HomotopyGroup(C,n)

Inputs a cat-1-group C and an integer n. It returns the nth homotopy group of C.

HomotopyModule
HomotopyModule(C,2)

Inputs a cat-1-group C and an integer n=2. It returns the second homotopy group of C as a G-module (i.e. abelian G-outer group) where G is the fundamental group of C.

ModuleAsCatOneGroup
ModuleAsCatOneGroup(G,alpha,M)

Inputs a group G, an abelian group M and a homomorphism \alpha\colon G\rightarrow Aut(M). It returns the Cat-1-group C corresponding th the zero crossed module 0\colon M\rightarrow G.
MooreComplex
MooreComplex(C)

Inputs a cat-1-group C and returns its Moore complex [M_1 \rightarrow M_0] as a list whose single entry is a homomorphism of groups.
NormalSubgroupAsCatOneGroup
NormalSubgroupAsCatOneGroup(G,N)

Inputs a group G with normal subgroup N. It returns the Cat-1-group C corresponding th the inclusion crossed module N\rightarrow G.