1#@local G,c5,d,eo,es,ess 2gap> START_TEST("oprt.tst"); 3gap> c5:=CyclicGroup(IsPermGroup,5);; 4gap> d:=Combinations([1..5],2);; 5gap> eo:=ExternalOrbit(c5,d,[1,2],OnSets); 6[ 1, 2 ]^G 7gap> IsTransitive(eo); 8true 9gap> Transitivity(eo); 101 11gap> IsPrimitive(eo); 12true 13gap> Blocks(eo); 14[ [ [ 1, 2 ], [ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ] ] ] 15gap> es:=ExternalSet(c5,d,OnSets);; 16gap> ess:=ExternalSubset(c5,es,[[1,2]],OnSets);; 17gap> IsTransitive(es); 18false 19gap> IsTransitive(ess); 20true 21gap> IsPrimitive(ess); 22true 23gap> Blocks(ess); 24[ [ [ 1, 2 ], [ 1, 5 ], [ 2, 3 ], [ 3, 4 ], [ 4, 5 ] ] ] 25gap> G:=AbelianGroup(IsPermGroup,[12,12]);; 26gap> eo:=ExternalOrbit(G,[1..24],1,OnPoints);; 27gap> IsTransitive(eo); 28true 29gap> Blocks(eo); 30[ [ 1, 5, 9 ], [ 2, 6, 10 ], [ 3, 7, 11 ], [ 4, 8, 12 ] ] 31gap> RepresentativesMinimalBlocks(eo); 32[ [ 1, 5, 9 ], [ 1, 7 ] ] 33gap> MaximalBlocks(eo); 34[ [ 1, 3 .. 11 ], [ 2, 4 .. 12 ] ] 35gap> eo:=ExternalOrbit(G,[1..12],1,OnPoints); 361^G 37gap> IsTransitive(eo); 38true 39gap> Blocks(eo); 40[ [ 1, 5, 9 ], [ 2, 6, 10 ], [ 3, 7, 11 ], [ 4, 8, 12 ] ] 41gap> STOP_TEST( "oprt.tst", 1); 42