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. Wake dynamic mode analysis enables us to capture different modes and their contributions to the kinetic energy distribution within the region of interest. For DrivAer geometry, at high Reynolds number, we observed quasi-steady wake deviation, vortex shedding, and bubble pumping as the most dominant fluctuation modes. These findings would help us characterize the average and principal unsteady features of wake in order to control the flow field and accurately predict the aerodynamic characteristics of a ground vehicle. We also observed that the center-plane flow-fields can be reconstructed, with an error less than 2%, using only two dominant modes.