You can delete a class by opening your class settings and scrolling down to "Archive" (the last option in the menu, under "Advanced").
Archiving is a permanent action. It deletes the class and its information, so it will no longer appear in your "My Classes" list and cannot be unarchived. However, you can always import your customizations from an archived class later on.
Although archiving a class also archives student characters, it does not delete their student accounts.