Congruences for the class numbers of real cyclic sextic number fields

Let K-6 be a real cyclic sextic number field, acid K-2, K-3 its quadratic and cubic subfield. Let h(L) denote the ideal class number of field L. Seven congruences for h(-) = h(K-6)/(h(K-2)h( K-3)) are obtained. In particular, when the conductor f(6) of K-6 is a prime p, Ch(-) = Bp-1/6 B5(p-1)/6 (mod p), where C is an explicitly given constant, and B-n is the Bernoulli number. These results on real cyclic sextic fields are an extension of the results on quadratic and cyclic quartic fields.