Managers have the ability to turn off all public comments and private replies for all posts on a per-group basis.

To disable comments & private replies, navigate to the group settings by clicking the gear icon on the gray navigation bar.

Then, select the Content tab of the settings.

When public comments and/or private replies are toggled off (in the left position), this will not allow members or managers to reply to any posts in the group. 

This can be used in conjunction with turning off other post types to create a group that serves as a Community Announcements group--managers can share important updates. 

To learn more about general member posting permissions, check out this help article.