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We report the magnetoresistance (MR),de Haas-van Alphen (dHvA) oscillations and the electronic structures of single-crystal PtGa.The large unsaturated MR is observed with the magnetic field B ||[111].Evident dHvA oscillations with the B ||[001]configuration are observed,from which twelve fundamental frequencies are extracted and the spin-orbit coupling (SOC) induced band splitting is revealed.The light cyclotron effective masses are extracted from the fitting by the thermal damping term of the Lifshitz-Kosevich formula.Combining with the calculated frequencies from the first-principles calculations,the dHvA frequencies F1/F3 and F11/F12 are confirmed to originate from the electron pockets at Γ and R,respectively.The first-principles calculations also reveal the existence of spin-3/2 Rarita-Schwinger-Weyl fermions and time-reversal doubling of the spin-1 excitation at Γ and R with large Chern numbers of ±4 when SOC is included.