Hey Craig!

Yes, you can have a group's post moderated. To do so, simply do this:

1) Go to EasySocial>Groups>Categories and choose your desired group.
2) Go to Custom Fields tab and click/drag the Post Moderation field into the group's form.
3) Save the settings and go to the EasySocial>Groups>Groups and choose the group that you have changed the settings. You should be able to find the Post Moderation settings there. Enable it.
4) Save the settings.
5) You can also set the group's admin in the Members tab. Only admins can moderate posts.

That's it! I hope this helps!