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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
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