An official with Community College of Allegheny County -- where TMC graduated with high honors on May 16 -- told us the gunman was a member of Phi Theta Kappa ... which is an honors society, and he was part of the local chapter.

If you go to their Facebook page, you'll see they were pretty involved with extracurriculars -- getting together for events, attending conventions and talking shop in and around the school. From the looks of it ... there are no photos of Thomas on their socials.

TMC majored in Engineering Science and graduated with an Associate's degree in Science ... while at the school from 2021 through May of this year. This jibes with what we already knew about him -- namely, that he went to a technical training school during high school.

Also of note ... we're told there are no records relating to any disciplinary, student conduct or security-related incidents involving Thomas -- so as far as they can see, not a troublemaker.

There's more ... TMZ has learned that Thomas was actually on his way to a 4-year university -- this after being accepted into two different schools after graduating from CCAC. We've confirmed he got into the University of Pittsburgh and Robert Morris University ... and that he was planning to attend Robert Morris.

A rep for RMU tells us ... "While Thomas Matthew Crooks had not yet attended classes at the university, we can confirm that he had planned to enroll beginning in Fall 2024. We have been in touch with law enforcement and stand ready to assist in their investigation."

They add, "Our hearts go out to former President Trump, the family of Mr. Corey Comperatore, and anyone physically or emotionally harmed by this tragic event. We stand against violence in all its forms and are committed to fostering a safe and supportive community for all."

As we've reported ... the gunman was killed on Saturday, moments after he opened fire on the ex-Prez during a campaign rally in Pennsylvania ... an incident that is being highly scrutinized for massive security failures.