  It is proved that c = 689347 = 31*37*601 is the smallest conductor of a
cyclic cubic number field K whose maximal unramified pro-3-extension E =
F(3,infinity,K) possesses an automorphism group G = Gal(E/K) of order 6561 with
coinciding relation and generator rank d2(G) = d1(G) = 3 and harmonically
balanced transfer kernels kappa(G) in S(13).
