[en] At the proton energy of E_p = 7.4 MeV, the double-differential cross sections for the reaction ²⁷Al(p, α₁γ)²⁴Mg were measured for 11 values of the alpha-particle emission angle in the range of θ_α = 30°–160°(lab). All even components of the density-matrix spin-tensors were reconstructed for the oriented ²⁴Mg nucleus in the 2⁺ state at 1.369 MeV, and the polarization features of this nucleus, including the populations of magnetic sublevels of the nucleus for all spin projections, multipole-moment orientation tensors, and the quadrupole and hexadecapole tensor polarizations, were determined. Relevant experimental results were compared with their counterparts calculated for the triton-pickup mechanism within the coupled-channel method and in the statistical limit of the compound-nucleus model.