We present a symmetry-based method for the efficient calculation of energy levels in hexagonal GaN/AlN quantum dots within the framework of a kp model. The envelope functions are expanded into a plane wave basis on a hexagonal lattice and the group projector method is used to adapt the basis to exploit the symmetry, resulting in block diagonalization of the corresponding Hamiltonian matrix into six matrices and classification of the states by the quantum number of total quasi-angular momentum. The method is applied to the calculation of the electron and hole single-particle states in a quantum dot superlattice. The selection rules for absorption of electromagnetic waves in the dipole approximation are established and the intraband optical absorption matrix elements are found. Good agreement with the available experimental data on intraband optical absorption is found.