Many simulations of protostellar collapse make use of a grey treatment of radiative transfer coupled to the hydrodynamics. However, interstellar gas and dust opacities present large variations as a function of frequency. In this paper, we present multigroup radiation hydrodynamics simulations of the collapse of a spherically symmetric cloud and the formation of the first and second Larson cores. We have used a non-ideal gas equation of state as well as an extensive set of spectral opacities. Small differences between grey and multigroup simulations were observed. The first and second core accretion shocks were found to be super- and sub-critical, respectively. Varying the initial size and mass of the parent cloud had little impact on the core properties (especially for the second core). We finally present early results from 3D simulations that were performed using the RAMSES code.