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Put $i=\\sqrt{-1}$, $d=2p_1p_2$ and $k =Q(\\sqrt{d}, i)$. Let $k_2^{(1)}$ be the Hilbert 2-class field of $k$ and $k^{(*)}=Q(\\sqrt{p_1},\\sqrt{p_2},\\sqrt 2, i)$ be its genus field. Let $C_{k,2}$ denote the 2-part of the class group of $k$. The unramified abelian extensions of $k$ are $K_1=k(\\sqrt{p_1})$, $K_2=k(\\sqrt{p_2})$, $K_3=k(\\sqrt{2})$ and $k^{(*)}$. 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