Fusionclass:=function(G,g)
local a,aut,l;
l:=[];
aut:=AutomorphismGroup(G);
for a in aut do
  Add(l,Image(a,g));
od;
return Set(l);
end;

autocenter:=function(G)
local M,N,g;
M:=Filtered(G,g->Size(Fusionclass(G,g))=1);
N:=Subgroup(G,M);
return N;
end;