As I wrote in another post, Facebook considers copyright and trademarks much more seriously than YouTube. They close Groups and ban Accounts even after only 2 copyright/trademark infringements.
I've closed groups with millions of followers in the past, because they were freebooting videos from my YouTube channels. Later I received e-mail complaints from the group owners that not only their groups are closed, but also their accounts and they can't register new accounts to keep in touch with friends/family, because Facebooks blocks them on sign-in.
Only way to restore your group/account is to contact the person who filed the copyright complaint and ask him/her to manually retract the claims. Only after the claims are retracted, it is possible to restore your group/account. Else, Facebook has enough data to know when you sign-in again, if you use similar or close credentials (phone, region, ID etc.).
BTW it wasn't me who closed your group, so I can't help.