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gap> hexagon := SplitCayleyHexagon(5);
H(5)
gap> Order(hexagon);
[ 5, 5 ]
gap> g := CollineationGroup( hexagon );
#I for Split Cayley Hexagon
#I Computing nice monomorphism...
#I Found permutation domain...
G_2(5)
gap> incgraph := IncidenceGraph( hexagon );;
#I Computing incidence graph of generalised polygon...
gap> Diameter(incgraph);
6
gap> Girth(incgraph);
12
gap> points := Points(hexagon);
<points of H(5)>
gap> lines := Lines(hexagon);
<lines of H(5)>
gap> iter := Iterator(points);
<iterator>
gap> x := NextIterator(iter);
<a point in H(5)>
gap> Display(x);
[.1.....]
gap> UnderlyingObject(x);
<cvec over GF(5,1) of length 7>
gap> onx := Lines(x);
<shadow lines in H(5)>
gap> l := Random(onx);
<a line in H(5)>
gap> onl := Points(l);
<shadow points in H(5)>
gap> List(onl, t -> DistanceBetweenElements(x,t));
[ 0, 2, 2, 2, 2, 2 ]
gap> stabl := FiningStabiliser(g, l);
<projective collineation group of size 1500000 with 3 generators>
gap> gl := Action(stabl, onl);
Group([ (1,6,5,4,3), (1,4,3,6), (1,5,4,3,6,2) ])
gap> StructureDescription(gl);
"S5"
gap> Transitivity(gl);
3
[ Dauer der Verarbeitung: 0.15 Sekunden
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