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A magnetohydrodynamic model of irradiating Z-pinch is the basis of a 2-D (in Euler cylindrical coordinates r-z) computer code FLUX-rz developed in VNIIEF (Russia). Earlier, the code considered the thermal radiation transfer in one-group (gray) diffusion approximation. This paper presents a modification of the FLUX-rz code in which we realized a multigroup diffusion model of the radiation transfer. Efficiency of an improved algorithm has been demonstrated by sample calculations of Shot 52 and Shot 567 on Z-machine at Sandia National Laboratories (U.S.).