vector := function(g, h)
local ind, s, list, dc, i, t;
ind := Index(g, h);
s := Size(DoubleCosets(g, h, h));
list := [];
dc := DoubleCosetRepsAndSizes(g, h, h);
for i in [1..s] do
t := Index(h, Intersection(h, h^dc[i][1]));
Add(list, t);
od;
Sort(list);
return Reversed(list);
end;;

prob := function(list)
local length, prod, i, t;
length := Length(list);
prod := 1;
for i in [1..length] do
t := list[i];
prod := prod*Factorial(t)/(t^t);
od;
return prod;
end;;

tp := function(g)
local auxlist, subreps, h;
auxlist := [];
subreps := Filtered(List(ConjugacyClassesSubgroups(g), Representative), 
x-> not IsNormal(g, x));
if Size(subreps) = 0 then
return 1;
fi;
for h in subreps do
Add(auxlist, prob(vector(g, h)));
od;
Sort(auxlist);
return auxlist[1];
end;;

tp_with_vector := function(g)
local auxlist, subreps, h;
auxlist := [];
subreps := Filtered(List(ConjugacyClassesSubgroups(g), Representative), 
x-> not IsNormal(g, x));
if Size(subreps) = 0 then
return 1;
fi;
for h in subreps do
Add(auxlist, [prob(vector(g, h)), vector(g, h)]);
od;
Sort(auxlist);
return auxlist[1];
end;;