How to join an existing friend group at school?

I’m a 15 year old girl. Me and my school friend group had a huge argument recently and I cut them off because we were having a lot of issues and it was toxic. But anyway, now I’m a bit of a loner, I only have one other friend who I sit with during breaks, so I really want to find a new group.

The problems are, I’m a pretty awkward and quiet person when it comes to new people. I’ve also had many bad past experiences with friend groups who excluded/ignored/bullied me, which has made me scared to put myself out there & talk to new groups.

There is a particular group that I want to join. I have one mutual friend in the group, but I’m not close with anyone else in it and don’t know if they would even want me in the group. But they all seem really nice, fun, chill etc. How would I approach joining this group? Also I have a class with 1 other person in that group, she seems nice & sits by herself in class, but I haven’t talked to her. She’s the only one in the group I have a class with, I have no classes with anyone else.

I think the group don’t really have an opinion on me because we barely know each other but my mutual friend told me one of them said I seem really sweet. Anyways any advice regarding joining the friend group will be appreciated!