Symmetry unique atom coordinates

One thing I love about Mathematica is how easily I can go from the name of a molecule to estimated coordinates of its atoms, with a command like

AtomList[Molecule[Entity["Chemical", "Toluene"]], All, {"AtomicNumber", "AtomCoordinates"}]

(although, oddly enough, "AtomCoordinates" does not appear in the "AtomList" documentation)

I can also easily get the point group:

Molecule[Entity["Chemical", "Toluene"]]["PointGroup"]

This is exciting because this is exactly the input I need to run GAMESS and do quantum chemistry calculations (starting with a geometry optimization, of course, since JM has informed me that these coordinates are heuristic guesses).

But, really, this is not exactly the input that I need: what I really need are coordinates of only the symmetry-unique atoms.

I don’t suppose there’s a way to get coordinates of symmetry-unique atoms, which I can use for GAMESS input? I know there’s some functions related to point group symmetry, but I haven’t thought of how to do it.