We propose the complex group theoretical Clebsch-Gordan coefficients as a novel origin of CP violation. This is manifest in our model based on SUSY SU(5) combined with the double tetrahedral group, T', as the family symmetry. Due to the presence of the doublet representations in T', there exist complex CG coefficients, leading to explicit CP violation in the model. Because of the Georgi-Jarlskog relations, the prediction for theta13 is determined entirely by the Cabibbo angle and the CG coefficients of T' and SU(5). In addition, the model gives rise to a sum rule involving the solar mixing angle, the Cabibbo angle, and the leptonic Dirac CP phase. The predicted leptonic Dirac CP phase of 227 degrees is very close to the T2K best fit value, and the predicted CP violation measures in the quark sector are consistent with the current experimental data. Sufficient amount of baryon number asymmetry is obtained through leptogenesis. Since the low energy phases are the only non-vanishing phase predicted in the lepton sector, there is a connection between leptogenesis and low energy leptonic CP violating processes in our model.