# usage MyChain(group) or MyChain(group,base)
MyChain:=function(arg)
local G,c,d,i,s,t,g;
  G:=arg[1];
  if Length(arg)=1 then
    c:=StabChain(G);
  else
    c:=StabChain(G,rec(base:=arg[2]));
  fi;
  d:=rec(generators:=GeneratorsOfGroup(G));
  t:=d;
  while Length(c.generators)>0 do
    d.orbit:=[c.orbit[1]];
    d.transversal:=[];
    d.transversal[c.orbit[1]]:=();
    i:=1;
    while i<=Length(d.orbit) do
      for g in d.generators do
	s:=d.orbit[i]^g;
	if not s in d.orbit then
	  Add(d.orbit,s);
	  d.transversal[s]:=d.transversal[d.orbit[i]]*g;
	fi;
      od;
      i:=i+1;
    od;

    s:=d;
    c:=c.stabilizer;
    d:=rec(generators:=c.generators);
    s.stabilizer:=d;
  od;
  return t;
end;