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

gap> n:=5;; G:=PrimitiveGroup(5,1);; a:=Transformation( [ 1, 3, 2, 2, 2 ] );;
gap> gens:=List(GeneratorsOfGroup(G), x-> AsTransformation(x, n));;
gap> S:=Semigroup(Concatenation(gens, [a]));;
gap> Size(S);
360
gap> I:=Idempotents(S, 3);;
gap> T:=Semigroup(I);
<semigroup with 10 generators>
gap> Size(T)=Size(S)-Size(G);
false