A detailed study of the magnetic and magnetocaloric properties of the garnet compound is carried out using x-ray diffraction, magnetization, heat capacity, and neutron diffraction measurements as well as ab initio band-structure calculations. This compound manifests two successive magnetic transitions at and . Neutron powder diffraction experiments reveal that these two transitions correspond to the collinear and noncollinear antiferromagnetic ordering of the nonfrustrated and frustrated sublattices, respectively. The interactions within each of the Cr and Mn sublattices are antiferromagnetic, while the intersublattice interactions are ferromagnetic. The H-T phase diagram is quite complex and displays multiple phases under magnetic field, which can be attributed to the frustrated nature of the spin lattice. shows a large magnetocaloric effect with a maximum value of isothermal entropy change J/kg K and adiabatic temperature change for a field change of 7 T. Further, a large value of the relative cooling power ( J/kg) demonstrates the promise of using this compound in magnetic refrigeration.