WhiteheadPermGroup( X )
This function first calls WhiteheadGroupTable, see
refWhiteheadGroupTable. These lists are then converted to
permutations, producing a permutation group which is effectively a
regular representation of the group. A field .WhiteheadPermGroup is
added to X.actorSquare and a field .genpos is added to
D = X.derivations. The latter is a list of the positions in
D.genimageList corresponding to the chosen generating elements. The
group is given the name WG(<name of X>).
For an example, we return to the crossed module XSC = [c3->s3]
obtained from the cat1-group SC in section refCat1Select which
has Whitehead group and automorphism group isomorphic to s3.
gap> WG := WhiteheadPermGroup( XSC );
WG([c3->s3])
gap> XSC.derivations.genpos;
[ 2, 4 ]
gap> Elements( WG );
[ (), (1,2,3)(4,6,5), (1,3,2)(4,5,6), (1,4)(2,5)(3,6),
(1,5)(2,6)(3,4), (1,6)(2,4)(3,5) ]
GAP 3.4.4