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gap> pg := PG(3,4);
ProjectiveSpace(3, 4)
gap> coll := CollineationGroup(pg);
The FinInG collineation group PGammaL(4,4)
gap> gens := GeneratorsOfGroup(coll);
[ < a collineation: <cmat 4x4 over GF(2,2)>, F^0>,
< a collineation: <cmat 4x4 over GF(2,2)>, F^0>,
< a collineation: <cmat 4x4 over GF(2,2)>, F^2> ]
gap> UnderlyingMatrix(gens[2]);
<cmat 4x4 over GF(2,2)>
gap> Unpack(last);
[ [ Z(2)^0, 0*Z(2), 0*Z(2), Z(2)^0 ], [ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ],
[ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ], [ 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ] ]
gap> as := AffineSpace(3,4);
AG(3, 4)
gap> coll := CollineationGroup(as);
AGammaL(3,4)
gap> GeneratorsOfGroup(coll);
[ < a collineation: <cmat 4x4 over GF(2,2)>, F^0>,
< a collineation: <cmat 4x4 over GF(2,2)>, F^0>,
< a collineation: <cmat 4x4 over GF(2,2)>, F^0>,
< a collineation: <cmat 4x4 over GF(2,2)>, F^2> ]
gap> gp := SplitCayleyHexagon(3);
H(3)
gap> coll:= CollineationGroup(gp);
#I for Split Cayley Hexagon
#I Computing nice monomorphism...
#I Found permutation domain...
G_2(3)
gap> GeneratorsOfGroup(coll);
[ < a collineation: <cmat 7x7 over GF(3,1)>, F^0>,
< a collineation: <cmat 7x7 over GF(3,1)>, F^0>,
< a collineation: <cmat 7x7 over GF(3,1)>, F^0>,
< a collineation: <cmat 7x7 over GF(3,1)>, F^0>,
< a collineation: <cmat 7x7 over GF(3,1)>, F^0> ]
gap> egq := EGQByqClan(LinearqClan(3));
#I Computed Kantor family. Now computing EGQ...
<EGQ of order [ 9, 3 ] and basepoint 0>
gap> coll := CollineationGroup(egq);
#I Computing incidence graph of generalised polygon...
#I Using elation of the collineation group...
<permutation group of size 26127360 with 6 generators>
[ Dauer der Verarbeitung: 0.20 Sekunden
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