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### symmetric group: get back conjugacy class from its generators

The function below returns a list r of elements of the symmetric group that leave a certain polynomial f fixed. I know (by the properties of f that I'm not specifiying here) that the list of g's that leave it fixed generate one of the 11 conjugacy subclasses of S(4). What is the best way to output from my code below a number between 1 and 11 that corresponds to such subclass?

R = PolynomialRing(QQ, 4, ["q1","q2","q3","q4"])
q1,q2,q3,q4 = R.gens()
f = 1 + q1 +q2 # in general, it is a polynomial with unit coefficients in the ring R
G = SymmetricGroup(4)
cl = G.conjugacy_classes_subgroups()
r = []
for g in G:
if (f * g) == f: r.append(g)
return r