We investigate the properties of electronic states and optical transitions in hexagonal GaAs quantum dots within Al0.3Ga0.7As nanowires, grown in axial direction [111]. Such dots are particularly interesting due to their high degree of symmetry. A streamlined postsymmetrization technique based on class operators (PTCO) is developed which enables one to benefit from the insight brought by the maximal symmetrization and reduction of fields (MSRF) approach reported by Dalessi et al. [Phys. Rev. B 81, 125106 (2010)], after having solved the Schrodinger equation. Definite advantages of the PTCO are that it does not require modification of existing code for the calculation of the electronic structure, and that it allows to numerically test for elevated symmetries. We show in the frame of a four-band k . p model that despite the fact that the D-6h symmetry of the nanostructure is broken at the microscopic level by the underlying zinc-blende crystal structure, the effect is quite small. Most of the particularities of the electronic states and their optical emission can be understood by symmetry elevation to D-6h and the presence of approximate azimuthal and radial quantum numbers.