[qwaszx]

How do you know when to assign symbols indicating degeneracy (E, T etc) to orbitals under a certain symmetry?

For example, for a point group (with a C4 major axis and 4 perpendicular C2s) there are 7 symmetry species but there are 4 pairs which get the same Mulliken symbol: s,dz^2, px&py, dx^2-y^2&dxy, as well as dyz&dxz. Do they all get called e in the irreducible representation, or can they be treated as  singly degenerate.  Also, while the pairs each share a Mulliken symbol, there is slightly different symmetry in each pair except the A1 (for example, dxz is symmetric to one sigma-d' (a) and antisymmetric to another sigma-d'(b) while dyz is symmetric to b but not to a).

Thanks, I've only seen examples which involve major rotation axes that have positions which do not fall on the x,y,z axes such as D3h.