JIRA permits the creation of groups with empty names.

How to reproduce:

1. Click on "Group Browser"
2. Just click "Add Group" leaving the field blank.

And worst, you cannot delete that group anymore.

Workaround:

Please, create a database backup before manually changing it!

Delete the group manually in database.

DELETE FROM groupbase WHERE groupname LIKE ''

JIRA needs to be restarted in order to apply this change.