I've struggled to use the group pages well in the past. I have a difficult time figuring out exactly what to do with them. In the past, Brandon and I have used group pages to separate classes: for example, in the Gender in Culture/Gender in History course, we make one group for Gender in Culture with all students and another group for Gender in History just for those few students taking the extra seminar. While the group functionality was great for that, the actual group page was simply bare and I never really figured out what to do with it; it would just have some generic "This is the group for students in Gender in History" sentence on it and that was it.
I think I would like for it to be more like a hub for announcements, a true gathering place for group members. But I'm unsure how to design that. Maybe it requires a broader redesign, like in a user's dashboard having "quick links" to the group pages for all a user's groups (though I guess the groups tab does that...) and some system for allowing some/all members of a group to post on that group page, almost wiki-fying it but I don't think I want to go quite that far.