the one she belongs to is called a fraternity

They should call it a fratority - especially if she's fraternizing with any of the brothers. :)

P.S. A Google search reveals that Theta Sigma thought of this at least 3 years before I did:

Extract from Theta Sigma website:

The term ?fratority,? combining fraternity and sorority, was adopted to demonstrate that ?some members have penises and others do not.?

http://snipurl.com/fxa4