Green’s Dictionary of Slang

fratty adj.

also fratastic, fratstar
[frat n. (1) + sfx -y/SE fraternity + fantastic/star]

(US campus) pertaining to fraternity life.

[US]Eble Sl. and Sociability 33: Another frequently used suffix is adjective-forming y [...] College slang has dorky, fratty, freaky, geeky, grooty, lunchy, spacey, squirrelly, and others.
[US]Eble Campus Sl. Nov. 3: fratty – epitomizing fraternity behavior and dress. Also fratastic, fratstar.
[US]Eble Campus Sl. Apr. 3: fratastic [...] Those croakies (holders for sunglasses) are so fratastic.
[US]C. Eble (ed.) UNC-CH Campus Sl. Spring 2014 Fall .
[US]M. Reed ‘Hawk Tuah and the Zynternet’ 8 July 🌐 [A] broad community of fratty, horndog, boorishly provocative 20- and sometimes (embarrassingly) 30-somethings [...] has emerged to form a newly prominent online subculture.

In compounds

fratty-bagger (n.) (also bag, bagger) [bags n.2 (1), i.e. the style of baggy trousers worn]

(US campus) a stereotypical fraternity member.

[US]Eble Campus Sl. Mar. 2: fratty-bagger – someone who [...] loves fraternity life: Fratty baggers always dress the same: corduroy jackets, crew-neck sweaters, and topsider shoes.
[US]Eble Campus Sl. Fall 1: bagger – a member of a fraternity.
[US]Eble Campus Sl. Fall 3: fratty-bagger – fraternity member, usually dressed in Izod shirts and baggy khakis.
[US]Eble Campus Sl. Fall 1: bag – a fraternity member.
[US]Eble Campus Sl. Mar. 1: bagger – man who wears his boxer shorts so they hang out below his regular shorts.
[US]Eble Sl. and Sociability 64: ‘A stereotypical fraternity member’ has for years been called a fratty-bagger or a bagger because of a style of pants once fashionable.