When a member joins a group, he or she is assigned the Member role by default. Members are able to contribute to the group’s discussions, activity feeds, and view other group members.
When a group member is promoted to be a moderator of the group, the member gains the ability to delete any activity feed items that may violate group rules, excluding those posted by organizers.
Organizers have total control over the contents and settings of a group. That includes all the abilities of moderators, as well as change group status from public to private, change the group photo, manage group members, and delete the group.