We prove, by a direct dimensional reduction and an explicit construction of the group manifold, that the nonlinear sigma model of the dimensionally reduced three-dimensional A = R magical supergravity is F 4(+4) /(U Sp(6)×SU (2)). This serves as a basis for the solution generating technique in this supergravity as well as allows to give the Lie algebraic characterizations to some of the parameters and functions in the original D = 5 Lagrangian. Generalizations to other magical supergravities are also discussed.