The dual of a pseudocompact group refining the topology of the circle group

We present an example of a reflexive, pseudocompact, non-compact, monothetic group H such that the Pontryagin dual H ∧ of H is precompact, connected, Baire, and admits a continuous isomorphism onto the circle group. In addition, the countably compact subsets of both groups H and H ∧ are finite.