  Four $\ZZ_+$-bigraded complexes with the action of the exceptional
infinite-dimensional Lie superalgebra E(3,6) are constructed. We show that all
the images and cokernels and all but three kernels of the differentials are
irreducible E(3,6)-modules. This is based on the list of singular vectors and
the calculation of homology of these complexes. As a result, we obtain an
explicit construction of all degenerate irreducible E(3,6)-modules and compute
their characters and sizes. Since the group of symmetries of the Standard Model
$SU(3) \times SU(2) \times U(1)$ (divided by a central subgroup of order six)
is a maximal compact subgroup of the group of automorphisms of E(3,6), our
results may have applications to particle physics.
