This is a good metric for also determining usefulness

I am advocating testing assertions like this, as well as possible. Like you say, groups are interesting in the abstract because of their many connections to other branches of mathematics. I am not convinced that research in abstract group theory is useful. I suspect be that basic notions and (very basic) results of group theory are useful, but that further work motivated only by its connection to group theory (as opposed to some other domain where the language of groups can be applied) has little value.