It's legit.
Thank you for verifying before joining. I am one of the admins on the page.
The USAFA Parent Liaison is a member of the group as well.
You will be asked for proof that your candidate has been offered an appointment because we vet all members to ensure OpSec and PerSec (operational and personal security). The group is "private". It is only for parents/guardians. Extended family, siblings, girl/boyfriends, etc. are not admitted into the group.
We do not have an "official email address" because, although we have USAFA and AOG representation on those Facebook pages, it is not USAFA run.
I am posting the links to the USAFA Parent Support Pages which list the Facebook pages sanctioned by USAFA (once I have moderator approval).