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This paper is a continuation of []. We construct unconditionally several families of number fields with large class numbers. They are number fields whose Galois closures have as the Galois groups, dihedral groups $D_n$, $n=3,4,5$, and cyclic groups $C_n$, $n=4,5,6$. We first construct families of number fields with small regulators, and by using the strong Artin conjecture and applying some modification of zero density result of Kowalski-Michel, we choose subfamilies such that the corresponding $L$-functions are zero free...