  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
B//[001] configuration have been observed, from which twelve fundamental
frequencies are extracted and the spin-orbit coupling effect (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 (LK) formula.
Combining with the calculated frequencies from the first-principles
calculations, the dHvA frequencies F$_1$/F$_3$ and F$_{11}$/F$_{12}$ are
confirmed to originate from the electron pockets at $\Gamma$ and R,
respectively. The first-principles calculations also reveal the existence of
spin-3/2 RSW fermion and time-reversal (TR) doubling of the spin-1 excitation
at $\Gamma$ and R with large Chern number $\pm4$ when SOC is included.
