I am assuming you are interested in Group Membership of a specific group.
Using the REST API you need to find the ID of the group to get the group membership.
To get the ID of the group, you need to first query all the groups, to retrieve the specific ID
Step 1. Get list of groups (Group Name, and Group ID)
Step 2. Query Membership of a specific group using the Group ID
Another option, would be to use the Repository Database instead, where you can also find this information.
Hope this helps