The Headmaster is presented as a fool. His attitude to Oxbridge is mocked by the other teachers. The boys share the teachers’ low opinion of him, for example when they trick him about their French lesson.
He is a hypocrite, as revealed by Dakin’s blackmailing him. The hypocrisy is also evident when the Headmaster does not want to sack Hector, asking him to resign instead, which makes it easier for him (the Head).
He is the stereotype of a particular kind of Headmaster, who is out of contact with the students, but pretends that he isn’t. The photograph in which he inserts himself while refusing to wait for Hector demonstrates this, particularly when the Headmaster rearranges the boys against their wishes.