Facebook groups are an extra feature in Facebook where you can communicate with select friends within the private space of your own page. You may find it useful to add a calendar to your group page if your group has a lot of upcoming important dates and schedule features. Facebook apps add extra functionality to your profile and pages; the calendar app will add a calendar to any page you have created.
Navigate to the Facebook App Directory, and then type "Calendar" into the "Search Apps" text box. Click "Search Apps."
Click "Add to my Page" toward the bottom of the left hand sidebar.
Click "Add to Page" next to the group page you want to add the app to. Click "Close."
You can only add an app to a group if you created the group -- apps can't be added by group members.