This whole situation is sad, but it doesn't sound like it's really the OPs fault or that she's the one causing it - she's just trying to figure out what to do. "She's the girl no one really likes" sounds harsh, but it sounds like an honest observation. Doesn't mean it's right, it just is what it is.
OP, just do what you can. Tell her you're kind of bored by yourself and see if she'll hang out with you, like she's doing you a favor.
Honestly - some of these responses don't seem grounded in reality. It's not always everyone else. I find it really hard to believe 30+ people aren't interested in this kid or that someone wouldn't be willing to hang out with her without some kind of reason. It only sounds like she mentioned that she doesn't have friends because she was giving a scenario for why her FP were different.