[GAP Forum] Minimal faithful permutation representation degree

[Saad]

Dear all,

Let G be any finite group, let $\mu G$ be the minimal faithful permutation representation degree of G, all research papers  I got trying to investigate whether the inequality $\mu G\times \mu H \leq \mu G +\mu H$ is strict or equality, where H is any other group, I did the following and wish somebody explain;


gap> a:=AlternatingGroup(5);:
gap> IsPerfectGroup(a);
true
gap> s:=OneSmallGroup(46,IsSolvable,true);
<pc group of size 46 with 2 generators>
gap> D:=DirectProduct(s,a);
<group of size 2760 with 4 generators>
gap> mua:=MinimalFaithfulPermutationDegree(a);
5
gap> mus:=MinimalFaithfulPermutationDegree(s);
23
gap> muD:=MinimalFaithfulPermutationDegree(D);
33

Thanks.