Based on Holden's description, what types of school is Pencey Prep?

From Holden's description we learn that Pencey Prep. is a very expensive boarding school. The school is big on football, but according to Holden they don't live up to their promise of molding boys into men. Girls weren't allowed at the school. and only senior boys could bring them to football games. Holden didn't understand the "no girl" rule and certainly didn't appreciate it.