gap&gt; g:=SymmetricGroup(4);
Sym( [ 1 .. 4 ] )
gap&gt; g1:=Subgroup(g,[(1,2,3)]);
Group([ (1,2,3) ])
gap&gt; g2:=Subgroup(g,[(1,4)]);
Group([ (1,4) ])
gap&gt; g3:=Subgroup(g,[(1,2,3,4)]);
Group([ (1,2,3,4) ])
gap&gt; cg:=CosetGeometry(g,[g1,g2,g3]);
CosetGeometry( SymmetricGroup( [ 1 .. 4 ] ) )
gap&gt; IsFlagTransitiveGeometry(cg);
false
gap&gt; cg2:=CosetGeometry(g,[g1,g2]);
CosetGeometry( SymmetricGroup( [ 1 .. 4 ] ) )
gap&gt; IsFlagTransitiveGeometry(cg2);
true
