Homogeneous CR-manifold in $\mathbb{C}^4$

In this paper we study holomorphically homogeneous model submanifolds CR-type (1, 3) complex space $\mathbb C^4$. One finds moduli space of five-dimensional model surfaces Bloom-Graham type ((2, 1), (3, 1), (4, 1)). It is shown that there exists unique model surface of this type with property of holomorphical homogeneous, which is equivalent to tube surface $\mathcal C$ with affin homogeneous base. One describes and classifies with respect to model surfaces the orbits relative to the group of holomorhical automorphisms of $\mathcal C$