I think the Raman tensor transforms as xy, yz , etc. So I would guess it transforms like E2g and some other representations (you have to consider the character table of the group). Cosnider a Stokes transition from the ground state which transforms as A1g, to a final state with 1 vibrational quantum of symmetry X. So
A1g x E2g x X must contain A1g or equivalently E2g x X must contain A1g. Similar analyses hold for the other components of the Raman tensor. E2g is certainly Raman active.