The transfer-matrix method is one of the well known methods used in photonics to analyze the propagation of electromagnetic waves through the layered periodic medium of a one-dimensional photonic crystal. The transfer matrix method was developed in accordance to Maxwell\'s equations which stated there exists, simple continuity conditions for the electric field across boundaries from one medium to the next. The TMM models a single period cell which can then be infinitely extended to include the whole structure. In this paper, we propose a formula which obtains the transfer matrix of the N cell structure using group theory. The novelty of the proposed formula lies in the fact that it calculates the system transfer matrix of the N cell periodic dielectric array directly easing the burden of not repeatedly performing the matrix multiplication operation.