Actor( C )
The actor of a cat1-group {cal C} is the cat1-group associated to the actor crossed module of the crossed module {cal X} associated to {cal C}. Its range is the automorphism group A and its source is A semidirect W where W is the Whitehead group.
gap> ActSC := Actor( SC );;
gap> Cat1Print( ActSC );
cat1-group Actor[c3^2|Xc2 ==> s3] :-
: source group has generators:
[ (4,6,5), (2,3)(5,6), (1,2,3)(4,6,5), (1,4)(2,5)(3,6) ]
: range group has generators:
[ (5,6,7), (1,2)(3,4)(6,7) ]
: tail homomorphism maps source generators to:
[ (5,6,7), (1,2)(3,4)(6,7), (), () ]
: head homomorphism maps source generators to:
[ (5,6,7), (1,2)(3,4)(6,7), (5,7,6), (1,2)(3,4)(6,7) ]
: range embedding maps range generators to:
[ (4,6,5), (2,3)(5,6) ]
: kernel has generators:
[ (1,2,3)(4,6,5), (1,4)(2,5)(3,6) ]
: boundary homomorphism maps generators of kernel to:
[ (5,7,6), (1,2)(3,4)(6,7) ]
: kernel embedding maps generators of kernel to:
[ (1,2,3)(4,6,5), (1,4)(2,5)(3,6) ]
: associated crossed module is Crossed module Actor[c3->s3]
GAP 3.4.4