Is it possible to take down a FB private group?

Not really if you are not a member you waste your time you can only report it with evidence but if you dont have access to that group with the beginning how you will get evidence ?!
 
If you see on there page that what they do is against FB rules, you can easily report them to FB support and they will take action.
 
You can still use the group link to submit a report directly to Facebook's system, even if you aren't a member of the group. If you are an administrator, the process is very simple, it takes only about 24 - 48 hours to receive a response from the system.
 
Just report the group to fb, and it doesn't matter it you are in the group or not, anyone could report
 
Reporting from the outside using just the Group ID rarely works unless the group name/description explicitly violates TOS. To actually get a private group taken down for selling prohibited goods, reports need to be submitted on specific posts from an account that is already inside the group.
 
Instead of mass reporting, you should document clear violations including links or screenshots and report them to Facebook there is a specific link provided for submitting such reports.
 
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