## Not all the semigroups <D(2*5), a>\D(2*5) are idempotent generated.
##
## GAP log file

gap> n:=5;; G:=PrimitiveGroup(5,2);; a:=Transformation( [ 1, 2, 3, 3, 3 ] );;
gap> gens:=List(GeneratorsOfGroup(G), x-> AsTransformation(x, n));;
gap> S:=Semigroup(Concatenation(gens, [a]));;
gap> Size(S);
365
gap> I:=Idempotents(S, 3);
[ Transformation( [ 1, 1, 1, 4, 5 ] ), Transformation( [ 1, 2, 2, 4, 2 ] ), 
  Transformation( [ 1, 2, 3, 1, 1 ] ), Transformation( [ 1, 2, 3, 3, 3 ] ), 
  Transformation( [ 1, 2, 4, 4, 4 ] ), Transformation( [ 1, 5, 5, 4, 5 ] ), 
  Transformation( [ 2, 2, 3, 2, 5 ] ), Transformation( [ 3, 3, 3, 4, 5 ] ), 
  Transformation( [ 4, 4, 3, 4, 5 ] ), Transformation( [ 5, 2, 3, 5, 5 ] ) ]
gap> T:=Semigroup(I);
<semigroup with 10 generators>
gap> Size(T)=Size(S)-Size(G);
false
gap> LogTo();