There should be a way for a group owner to delete the group. I made a group called "TEST" and I can't delete it. Someone delete that for me.
Also, there should be a way to know who is the group owner. Currently the only ways of knowing is to either ask a Tain admin/mod or by selecting the group in your profile and click Edit. If it goes to a page where you can edit the group, then you are the group owner. If it doesn't then you are not.
Third, I seem to be unable to add another group once I have already created the TEST group. I guess a group owner can't be owner of more than one group. This is more of a statement, not a request to alter it. Though having more groups might be a good idea since not everyone works with only their own group.