The aerodynamic drag reduction of a simplified vehicle, by means of a synthetic jet, is studied numerically. The numerical simulations are based on the Lattice-Boltzmann method. The synthetic jet is implemented in an open-loop control strategy. The performances of the actuator are evaluated in 3D configurations. Moreover, an extensive parametric study, by varying independently the momentum coefficient, the jet frequency and its location, is performed and discussed in details. Prior to the flow control analysis, the main features of the reference case, i.e. without control, are deeply investigated in terms of topology and dynamics as well. The optimal parameters of the synthetic jet are found and their influences onto the flow are emphasized by spectral analysis the near-wake unsteadiness and the complex interaction between the actuation and the flow. The drag reduction reaches 5% and 13% when the actuator is set upstream and downstream the corner between the roof and the rear window, respectively.