Hamiltonian Groups with Perfect Order Classes

A finite group is said to have "perfect order classes" if the number of elements any given either zero or a divisor group. The purpose this note describe explicitly Hamiltonian groups with perfect classes. We show that has classes if, and only it isomorphic direct product quaternion $8$, non-trivial cyclic $3$-group at most $2$. Theorem. $Q\times C_{3^k}$ C_{2}\times C_{3^k}$, for some positive integer $k$.