The classes are small (6-15 students) and we all get along really well.
On the first day of each class we create a secret group for the quarter so that we can discuss readings, assignments, and our opinion of the lecturer.
We all keep our laptops open during class and the group serves as a running commentary on the goings-on.
I can't imagine why you'd want a truly secret group otherwise. Not just closed, where non-members can't see the content, but secret, where non-members don't know the group exists.
// Edit: I'm also in a private group for computer-related majors at our school, kept private so we can talk about stuff we don't necessarily want getting back to administration. (Weak security, but better than public posts.)
It's not really secret in the sense that we try to keep extremely high levels of privacy on it, anybody can ask to join.
The secret group has a lock on its tab and says "Secret Group - Only members see the group, who's in it, and what members post". No one who I am friends with knows I'm in the group aside from people in the group. Not sure what more to say - it has a wall which is somewhat active, although content was better and more diverse when the group started, now it is mostly 1-2 boring friend-of-friend chatterboxes. It also had a chat room, although Facebook killed group chat rooms a few months ago.
There is actually no technical way possible for having a truly secret group.
Just don't go on when people are around.
BTW, the analogy of bank website isn't equally applicable because people don't hang out at their bank websites most of the time.