Sorry your daughter is having to deal with this, flu. Unfortunately, you’ll get the same thing in a lot of private schools, too. It’s why a lot of parents send their kids to religious schools, even if the parents aren’t religious — these schools tend to better enforce rules against bullying and they often discourage cliques (at least some do).
This is when parenting gets tough, IMHO. Nothing sucks more than watching your kid get hurt, emotionally or physically.
Hopefully, your daughter will meet a few really nice kids so she can ignore the mean ones. That’s the best defense.