The turbulent wake of a generic space launcher wind tunnel model with an underexpanded nozzle jet is investigated experimentally and numerically to gain insight into the variation of intricate wake flow phenomena of space vehicles at higher stages of the flight trajectory with increasing Mach number. The experiments are carried out at M-infinity = 3 and M-infinity = 6 in the Ludwieg tube test facility at the Institute of Fluid Mechanics at the Technische Universitat Braunschweig, while the corresponding time-resolved computations are performed by the Institute of Aerodynamics at RWTH Aachen University using a zonal RANS-LES approach. A strong alteration of the wake topology with increasing Mach number due to the changing pressure ratio at the nozzle exit is found. At M-infinity = 3 the moderate underexpansion rate of p(e)/p(infinity) approximate to 5 leads to a formation of a recirculation region with an elongated triangular cross-section reaching to the nozzle exit. At M-infinity = 6 a substantially stronger afterexpansion of the jet plume (p(e)/p(infinity) approximate to 100) causes the formation of a cavity region with a quadrangular cross-section. The stronger deflection towards the nozzle at M-infinity = 3 results in lower mean and rms wall pressure ratios than at M-infinity = 6. However, due to the higher freestream pressure value at the lower Mach number the relation of absolute values is reciprocal, making the lower supersonic regime more critical with respect to dynamic structural loads. This observation is confirmed by an overall good agreement between numerical and experimental data at characteristic positions on the base and nozzle wall. Furthermore, it was shown that undesired effects of the strut support in the wake are present along the whole circumference. For M-infinity = 3 the strut influence is found to be particularly intense. The spectral analysis of wall pressure fluctuations reveals fundamental differences in the dynamic behavior of the two investigated wake flow regimes. At M-infinity = 3, a dominant frequency range around Sr-D approximate to 0.2 associated with the inner dynamics of the recirculation bubble is found at the base, while on the nozzle a broad-band low-frequency content of substantially higher amplitudes is detected, which is a footprint of the graduate realignment of the turbulent shear layer along the nozzle wall. The spectra at M-infinity = 6 are characterized by several high-frequency sharp peaks at Sr-D >= 0.8. A strong correlation between the supported wind tunnel configuration and the axisymmetric free-flight case is found for the peaks at Sr-D approximate to 0.85 known to be caused by the radial flapping motion of the shear layer along the cavity.