A group is active if the current date (today) is between the group's start and end dates.
If the dates for your group are not yet active, it will show up in your Inactive Groups list like below:
Rewards and badges that you set up for a group cannot be redeemed unless the group is active.
To make a group active, make sure the Start Date is before today, and the End Date is sometime in the future.
You can do this by clicking the SETTINGS icon from Reading Circle --> My Groups.
Only reading logged between the group's START and END dates will count towards group minutes and pages. Only books started and finished between the group's start and end dates will appear on the group's statistics.