There is no such thing as the 'work related support group'.
You have the work-related activities group, often called the work group. For this you need to score 15 points and you may be expected to attend work-focused interviews.
Then you have the support group for claimants who are not expected to prepare for work. For this you need to pass a separate test that is not points based.
You can find more information in the Understanding ESA guide in the members' area.
