Google Groups cannot have calendars of their own, but you can create a subcalendar in your GoogleApps@UIC account for the group and share that with your group:
Please note that Google calendars cannot be embedded calendars in Google Groups. You also don’t have to enter the email addresses of the members of the group individually, just adding the group's email address is enough.
You can enable alarms or notifications of the meeting in the shared calendar. This cannot be done for everyone the calendar is shared with, each person in the group has to do this.
April 25, 2013