  We consider the only one known class of non-K\"ahler irreducible holomorphic
symplectic manifolds, described in the works of D. Guan and the first author.
Any such manifold $Q$ of dimension $2n-2$ is obtained as a finite degree $n^2$
cover of some non-K\"ahler manifold $W_F$ which we call the base of $Q$. We
show that the algebraic reduction of $Q$ and its base is the projective space
of dimension $n-1$. Besides, we give a partial classification of submanifolds
in $Q$, describe the degeneracy locus of its algebraic reduction, and prove
that the automorphism group of $Q$ satisfies the Jordan property.
