Local unitary classes of states invariant under permutation subgroups

The study of entanglement properties multi-qubit states that are invariant under permutations qubits is motivated by potential applications in quantum computing, communication, and metrology. In this work, we generalize the notions symmetrization, Dicke states, Majorana representation to alternating, cyclic, dihedral subgroups full group permutations. We use these tools characterize analyze their properties.