The point is that there are two separate upgrade: group level and group skill.

Group skill requires group level before it can be upgraded

Group skill increases the cap of group skill players can get, which is 5 x the level.

So a lv 7 group can have either lv 30 or 35 cap, lv 30 if it is a "new" lv 7 group that haven't upgraded its group skill. lv 35 if it have.

And as upgrading group skill cost almost as much as upgrading the group level, groups are going to spend quite a while at the "lv 30" point.