Quelle  stab_orbs_action1.include  Sprache: unbekannt

gap>; pg := PG(2,3);
ProjectiveSpace(2, 3)
gap>; conic := Set(Points(ParabolicQuadric(2,3)));;
gap>; coll := CollineationGroup(pg);
The FinInG collineation group PGL(3,3)
gap>; orb := Orbit(coll,conic,OnSetsProjSubspaces);;
gap>; Length(orb);
234
gap>; hom := ActionHomomorphism(coll,orb,OnSetsProjSubspaces);
<;action homomorphism>
gap>; perm := Image(hom);
<;permutation group with 2 generators>
gap>; Order(perm);
5616
gap>; NrMovedPoints(perm);
234
gap>; ps := SymplecticSpace(5,2);
W(5, 2)
gap>; coll := CollineationGroup(ps);
PGammaSp(6,2)
gap>; perm := Action(coll,Lines(ps),OnProjSubspaces);
<;permutation group with 4 generators>
gap>; NrMovedPoints(perm);
315