**Method 1:**
How to target Facebook groups and build an audience:
1. Create useful content, a video, or a link to a useful article (the content **must** be useful to the majority of people in the group in order for this to work).
2. Publish it on your Facebook page.
3. Hide it from your timeline.
4. Share the video, or post-url to the group and build engagement
Voila, you have now populated an audience of the active group members who interacted with your content.
**Method 2:**
Other than this you could always ask a group admin if he / she would allow you to tailor a custom offer to the group, I’ve had tons of admins approving this as it seems less commercial than “can i please spam your group with a generic offer”. Make some custom graphics and make it as easy as possible for the admins to approve it.