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
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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