  A generalization of the homological Poincare's operator was used to estimate
the dimension of the Lie algebra of infinitesimal holomorphic automorphisms of
an arbitrary germ of a real analytic hypersurface in ${\bf C}^4$. The following
alternative is proved: either this dimension is infinite, or it does not exceed
24. Value 24 takes place only for one of two nondegenerate hyperquadrics. If
the hypersurface is 2-nondegenerate at a generic point, then the dimension does
not exceed 17, and if the hypersurface is 3-nondegenerate at a generic point,
then the estimate is 20.
