Yes, EM has it's own auditing, although it is set up at a minimal level to begin with including EM login/logout. You would want to enable additional auditing to monitor this type of activity. See the Security Guide for more information:
In addition, since this is a target delete scenario, there's a query you can run to see the time of deletion, but not who deleted it:
select entity_type, entity_name, created_date, deleted_date
where entity_name = <group>;
Perhaps between the two you can deduce who was logged in at the time of the delete.