When you set up a Live session, you can extend it to other Groups in which you are an Instructor. This enables you to quickly involve multiple Groups in the Live session.
To add other Groups, click on the Add Group + button in the Create new Live dialog box; then select the Groups to add from the dropdown menu:
When you have created the Live session, it will be available on the Calendar of each invited Group and all the users who belong to those Groups will be invited.