You should be able to edit the description, group avatar, etc but I'm not sure how to do it...haven't used groups much. I suspect it's somewhere in your user control panel but I don't know at the moment (and need to head off for work tonight).
Maybe you could contact one of the guys that maintains one of the other groups and ask them how they're doing it. I know Carnivore maintains the CFS3 Blacksheep group and they've got a custom avatar and such set.