Page Group owners and administrators can change the page group owner. For Page Group owner, they need to open up the Page Group sharing settings, and from a user permission dropdown select "owner". This will promote the selected user as the owner and automatically demote the previous owner to a editor.
Administrators can do the same operation, but they first need to enter admin mode. This is done easily either by entering edit mode in the Page Group by enabling admin mode, or selecting to edit page from the Admin panel.