On basic invariants of some finite subgroups in $SL_3(\mathbf{C})$

The work is devoted to the study of algebras of invariants of finite unitary groups $G'=G\cap SL_3(\mathbf{C})$, where $G$ is a finite unitary irreducible primitive group generated by reflections in the unitary space $U^3$. It is known that the system of invariants of the group $G'$ that form an algebra is obtained from the system of invariants of the group $G$ that form the algebra by adding all semi-invariants of the group $G$ of a special form. In the paper, generators of the algebras of invariants of all the indicated groups $G'$ are constructed.