Lue( X )
This crossed module has the source of X
as source, and the
automorphism permutation group of X
as range.
gap> LXSC := Lue( XSC ); Crossed module Lue[c3->s3] gap> XModPrint( LXSC );Crossed module Lue[c3->s3] :- : Source group has parent ( c3^2
|
Xc2 ) and has generators: [ (1,2,3)(4,6,5) ] : Range group has parent ( PermAut(c3)xPermAut(s3) ) and has generators: [ (5,6,7), (1,2)(3,4)(6,7) ] : Boundary homomorphism maps source generators to: [ (5,6,7) ] : Action homomorphism maps range generators to automorphisms: (5,6,7) --> { source gens --> [ (1,2,3)(4,6,5) ] } (1,2)(3,4)(6,7) --> { source gens --> [ (1,3,2)(4,5,6) ] } These 2 automorphisms generate the group of automorphisms.
GAP 3.4.4