As the title implies, a service group - in this case, the 9th - provided support services: communications, supply, motor transport, etc. Headquarters and Headquarters Squadron was the principal executive and administrative element.
His MOS (Military Occupational Specialty), if you can determine it, will reveal what he was trained to do. His actually duties, however, may have been altogether different. (I interviewed for a position soon after separation. One question on a form was, "What did you do in the service?" I responded, "As told". That just about sums it up.)