Gholamreza Rafatneshan - Department of Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran
Yousef Zamani - Department of Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran

Let V be a unitary vector space. Suppose G is a permutation group of degree m and \Lambda is an irreducible unitary representation of G. We denote by V_{\Lambda}(G) the generalized symmetry class of tensors associated with G and \Lambda. In this paper, we prove the existence of orthogonal bases consisting of generalized decomposable symmetrized tensors for the generalized symmetry classes of tensors associated with unitary irreducible representations of group U_{۶n}, as well as dihedral and dicyclic groups.

Generalized symmetry classes of tensors, orthogonal basis, the group U_{۶n}, dihedral group, dicyclic group