  We investigate the electronic structure of the ternary iron selenide K$_{y}$%
Fe$_{1.6}$Se$_{2}$ by considering the spatial symmetry of the $\sqrt{5}% \times
\sqrt{5}$ vacancy ordered structure. Based on three orbitals of $% t_{2g}$,
which are believed to play major physics in iron-based superconductors, an
effective two-dimensional tight binding Hamiltonian is constructed with the
vacancy ordered structure being explicitly included. It is shown that the
constructed band model, when combined with generalized Hubbard interactions,
yields a spin susceptibility which exhibits both the block-checkerboard
antiferromagnetism instability and the stripe antiferromagnetism instability.
In particular, for large Hund's rule couplings, the block-checkerboard
antiferromagnetism wins over the stripe antiferromagnetism, in agreement with
the observation in experiments. We argue that such a model with correct
symmetry and Fermi surface structures should be the starting point to model
K$_{y}$Fe$_{1.6}$Se$_{2}$. The spin fluctuations at $\mathbf{q}$=($\pi ,\pi $)
suggest that interblock fluctuations of spins might play an important role in
the mechanism of superconductivity occurring in this system.
