The default group is determined by the default-group option in zPermissions's config.yml. Out-of-the-box, the default-group is named default. (If you change this option, be sure to reload your server or /permissions reload zPermissions.)
Regardless of whether or not you change the default group, when zPermissions starts up with a new database or a new flat-file, it will have no groups defined.
So one of the first things you'll probably want to do is create the default group.
If you left the default group alone:
/permissions group default create
Or if you changed it, for example, to guest:
/permissions group guest create
Once this is done, you can start assigning permissions to it.