<Chapter><Heading> Cat-1-groups</Heading> <Table Align="|l|" > <Row> <Item> <Index>AutomorphismGroupAsCatOneGroup</Index> <C> AutomorphismGroupAsCatOneGroup(G)</C> <P/> Inputs a group <M>G</M> and returns the Cat-1-group <M>C</M> corresponding th the crossed module <M>G\rightarrow Aut(G)</M>. </Item> </Row> <Row> <Item> <Index>HomotopyGroup</Index> <C>HomotopyGroup(C,n)</C> <P/> Inputs a cat-1-group <M>C</M> and an integer n. It returns the <M>n</M>th homotopy group of <M>C</M>. </Item> </Row> <Row> <Item> <Index>HomotopyModule</Index> <C>HomotopyModule(C,2)</C> <P/> Inputs a cat-1-group <M>C</M> and an integer n=2. It returns the second homotopy group of <M>C</M> as a G-module (i.e. abelian G-outer group) where G is the fundamental group of C. </Item> </Row> <Row> <Item> <Index>ModuleAsCatOneGroup</Index> <C> ModuleAsCatOneGroup(G,alpha,M)</C> <P/> Inputs a group <M>G</M>, an abelian group <M>M</M> and a homomorphism <M>\alpha\colon G\rightarrow Aut(M)</M>. It returns the Cat-1-group <M>C</M> corresponding th the zero crossed module <M>0\colon M\rightarrow G</M>. </Item> </Row> <Row> <Item> <Index>MooreComplex</Index> <C> MooreComplex(C)</C> <P/> Inputs a cat-1-group <M>C</M> and returns its Moore complex <M>[M_1 \rightarrow M_0]</M> as a list whose single entry is a homomorphism of groups. </Item> </Row> <Row> <Item> <Index>NormalSubgroupAsCatOneGroup</Index> <C> NormalSubgroupAsCatOneGroup(G,N)</C> <P/> Inputs a group <M>G</M> with normal subgroup <M>N</M>. It returns the Cat-1-group <M>C</M> corresponding th the inclusion crossed module <M> N\rightarrow G</M>. </Item> </Row> </Table> </Chapter>