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In this work, we study some properties of the Hickson Compact Groups (HCGs) using N-body simulations for the Generalized Dark Matter (GDM) model, described by three free functions, the sound speed, the viscosity and the equation of state. We consider three GDM models associated with different values of the free functions to neglect collisional effects. We constructed the initial seeds of our simulations according to the matter power spectrum of GDM linear perturbations, which hold a cut-off at small scales, and explored their effects on the non-linear structure formation at small and intermediate scales. We generated mock catalogues of galaxies for different models and classify HCGs by implementing an algorithm that adapts the original selection method for mock catalogues. Once the HCGs samples are classified, we analyzed their properties and compared them between models. We found that a larger amount of HCGs are counted in GDM simulations in comparison to CDM counts. This difference suggests that HCGs can proliferate within GDM despite the suppressed substructure, which indicates a possible modification in the HCG formation process within models where DM is not perfectly like CDM. Additionally, we identified different mechanisms of clustering, for models with a large amount of galaxy-halos self-agglomerate because of their abundance while models with fewer galaxy-halos need massive halos acting as a dominant potential well. Finally, by comparing distributions of different observables of simulated HCGs against observations, we found a good agreement in the intrinsic properties. However, a discrepancy in the velocity dispersion remains unsolved.