We set out to find the generic multipartite GHZ state from the multipartite entangled coherent states, which is composed of fermions. The figures of quasi-probability distribution of Wigner function of the GHZ state are worked out. The interaction energy of GHZ is computed through the eigenvalues of their eigenstates. When the phase factor changes from 0 to π, the variance of the configuration and interaction energy is analyzed. We compute the Wigner function using the Qotoolbox of Matlab computer language, which creates the orthogonal bases on the vector space. The way in which we compute the Wigner function is more convenient than others. Finally we validated the principle of identical particles, which is one of the assumptions of quantum mechanics.