We have performed a nuclear dynamics simulation to calculate photoelectron spectra and population profiles of benzene radical cation (C₆H$^+_6$) employing the parallelized Time Dependent Discrete Variable Representation (TDDVR) approach. For this purpose, we have considered two multi-state multi-mode model Hamiltonians of C₆H$^+_6$ with degeneracy among the electronic states: (a) One consists of three states and eight modes, which in turn leads to a five state thirteen mode Hamiltonian ($X^2$E$_{1g}$-$B^2$E$_{2g}$-$C^2$A$_{2u}$) due to the degeneracy; and (b) The other is constituted of three states and thirteen modes which is basically a five state twenty mode Hamiltonian ($B^2$E$_{2g}$-$D^2$E$_{1u}$-$E^2$B$_{2u}$) for the same reason. Since these electronic states are interconnected by several conical intersections in the vicinity of the Franck Condon region, it will be challenging to pursue such large dynamical calculation in the presence of nonadiabaticity among the electronic states. The spectral as well as population profiles calculated with the advent of TDDVR approach show reasonably good agreement with the results obtained by the Multi Configuration Time Dependent Hartree (MCTDH) methodology.