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We express the relative class number of an imaginary abelian num- ber field K of prime power conductor as a sort of Maillet determinant. Thereby we obtain explicit relative class number formulas for fields K of conductor p , p > 3 prime, and degree 2d = (K: Q) < 10, in terms of sums of 2d-power residues. In particular, tables are given for p < 10000.

The relative class numbers of imaginary cyclic fields of degrees 4,6,8, and 10