There are no default settings for the moderating group because different forums will assign different permissions depending on their needs.
I'd suggest that you set moderating permissions in this group that you want all of your moderators to have. For any moderating permissions that you want only specific individuals to have, you can assign these to those people when they are added as moderators in the ACP.
Do also bear in mind - when you give a permission at UserGroup level (eg to edit others' posts) then it will apply right across your entire board; it's not restricted to forums (nodes) to which the Moderator is allocated. In this respect, XF doesn't treat Moderators any differently to SuperModerators.
To so restrict extra abilities, they have to be set separately for each Moderator-Node combination, and not set at UserGroup level.