If a Group is assigned on Initial, it will not be displayed in the Activity Log unless it subsequently changes. Then the actual value would be recorded inside the action_desc field but it would have to be parsed out of the rest of the description.
I think you will have to enable auditing and then have a trigger that queries the audit_log table using the ticket persid for attr_name 'group' and then if your 'Group A' is in the attr_before_val or attr_after_val fields. Those could be be exact matches since that is the only value in the field.
The problem with that tickets created before auditing was enabled will not be in the table.
Just brainstorming at this point. Perhaps someone has already solved this.
J.W.