* Fraternity: This is the most common term, especially in North America. However, fraternities often have a broader scope than just a social club, often involving philanthropy, academics, and other activities.
* Social Club: A simple and straightforward term that applies if the club's primary focus is socializing.
* Gentlemen's Club: A more formal and less common term, possibly implying a more exclusive nature.
* The club may simply have a name that doesn't explicitly indicate its gender or purpose (e.g., "The Phoenix Club," "The Sigma Society").
The best term to use will depend on the context.