BuddyPress.org

It’s a bit tricky because, as far as I know, the group blog doesn’t really know that it’s associated with a particular group. From the point of view of the blog, it’s just a blog with multiple authors. Your best bet is probably to modify or hook into the groupblog plugin to make sure that, after it creates a new blog for the group, it also saves a piece of metadata in the wp_x_options table that associates the blog with a group. That way, in the post loop, you can use that metadata to get the group’s avatar.