gap> ag := AffineSpace(3,3);
AG(3, 3)
gap> points := Points(ag);;
gap> x := Random(points);
&lt;a point in AG(3, 3)>
gap> Display(x);
Affine point: [ Z(3), Z(3), 0*Z(3) ]
gap> planes := AsList( Planes(ag) );;
gap> p := Random(planes);
&lt;a plane in AG(3, 3)>
gap> Display(p);
Affine plane:
Coset representative: [ 0*Z(3), 0*Z(3), 0*Z(3) ]
Coset (direction): [ [ Z(3)^0, 0*Z(3), Z(3) ], [ 0*Z(3), Z(3)^0, 0*Z(3) ] ]
gap> g := CollineationGroup( ag );
AGL(3,3)