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The aerodynamic design optimization of a ground vehicle highly depends on the wake region behind it. Vehicle's wake and its instability have a major contribution to the drag, lift, and side forces experienced by the vehicle. In this paper, we investigate numerically the dynamic characteristics of the wake downstream of a realistic generic car model, DrivAer Fastback, at a Reynolds number of 4.8 million based on the free stream velocity and wheel-base as the characteristic velocity and length scales, respectively. Two methods, Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) are applied to symmetric the 2D plane, taken at the centerline of the geometry, to decompose the unsteady wake to its major dynamic modes. We simulated the flow field using a validated IDDES approach and then applied POD and DMD on the streamwise velocity field.