  We present a construction of genuinely entangled multipartite quantum states
based on the group theory. Analyzed states resemble the Dicke states, whereas
the interactions occur only between specific subsystems related by the action
of the selected group. The states constructed by this technique exhibit desired
symmetry properties and form a natural resource for less-symmetric quantum
informational tasks. We propose quantum circuits efficiently generating such
states, which in general have smaller complexity than the circuits necessary to
create fully symmetric entangled states.
