To be able to post to Facebook groups, you need to make sure you are an Admin level user on the Facebook group (same for pages), and you need to make sure you're authenticated for NetSocial to post to the group. It is not possible to post to groups your are not an Admin of at this time.
Here's how to authorize NetSocial to be able to post to Facebook groups.
In Facebook, while looking at the Group, go to Group Settings:
Click Add Apps:
Search for NetSocial:
This should resolve the permissions issue when trying to post to Facebook groups. If you have any questions, please reach out to the Success team at firstname.lastname@example.org.