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