SENSMG is a tool for calculating the first-order sensitivities of reaction-rate ratios, keff, and α in critical problems and reaction-rate ratios, reaction rates, and leakage in fixed-source problems to multigroup cross sections, isotope densities, material mass densities, and interface locations using the PARTISN multigroup discrete-ordinates code by implementing Generalized Perturbation Theory. SENSMG can be used for one-dimensional spherical and slab (r) and two-dimensional cylindrical (r-z) geometries. For fixed-source (leakage) problems, SENSMG relies on the MISC and/or SOURCES4C codes to compute neutron source rate densities from spontaneous fission and (α,n) sources. SENSMG is a combination of Python and Fortran and was developed under Linux. This computer code abstract describes all user inputs, the input file, and output files. This computer code abstract describes how SENSMG can be modified to support different computer platforms, PARTISN versions, or cross-section availability. Several verification problems are presented in which SENSMG results are compared with MCNP6, SCALE6.2, and direct perturbations (central differences). SENSMG is available at SENSMG can be modified to accommodate other deterministic transport codes that have an adjoint capability.