The Group field on the General tab of an event refers to the group of events the event belongs to, not a group of people in the event. 

To create an event group:
  1. Add the event group name to the Event Groups table.
  2. In Records, click Events.
  3. Open an event to add to the group.
  4. On the General Tab of the event record in the Group drop-down, select the event group added in step 1.
  5. Save and close the event.
  6. Repeat steps 2 through 5 for each event in the group.

For more information on using grouped events, please review the following Knowledgebase solutions: