early 14c., "body of men associated by common interest," from Old French fraternité (12c.), from Latin fraternitatem (nominative fraternitas) "brotherhood," from fraternus "brotherly," from frater "brother," from PIE root *bhrater- "brother." Meaning "state or condition of being as brothers" is from late 15c. College Greek-letter organization sense is from 1777, first in reference to Phi Beta Kappa.
<a href="https://www.etymonline.com/word/frat">Etymology of frat by etymonline</a>
Harper, D. (n.d.). Etymology of frat. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/frat