The groups management interface is located in the Groups. On this page, you can see a list of all groups on the site.
Even though groups are typically created by site users on the live site, you can create new groups in this section of the administration interface too. It can be done by clicking New group. See Editing groups for more information about creating and modifying groups in the administration interface.All pages can be set to be owned by a group. To do this, select a page from the content tree and go to Properties -> General. Then click Change next to Owned by group and choose a group from the drop-down list. This property is used to identify which group a page belongs to and is used by various group context sensitive web parts to display the correct content. It also influences the editing permissions of Group administrator widget zones.
See Allowing users to create groups for more information.