Any member of a group can invite others to the group, but only the group owner can remove them. By default, the group owner is the person who created the group but others can be assigned this role as well.
You can add and remove members from the group card.
You can use the Add Members button to navigate to add members to the page. If the group has more than 3 members, the Add Members button can be found on the View All Members page.
You can use the ... icon to remove group members.