I'm in my forties now but I was probably your daughter. I was a June baby so started in reception in January, and all the friendship groups were already formed. There was also a girl who I would probably label as the class leader - very extrovert, loud, and opinionated, whereas I was very shy and am an introvert, and she was the cause of my lack of friends.
She was also a bully - I was never hit, but she took the time every day to make sure I was alienated; I couldn't play with them because I was the only one with short hair, the only one with long socks, the only one with brown shoes etc. I was never invited to parties by people from school. This went on until a girl the same age as me who was going to go to my school moved next door when I was ten. The day she moved was the start of the school holidays, and we did nothing but play together all day every day. By the time it came round to go back to school she was already my friend, and nearly 40 years later she still is.
Things also improved when I went to secondary school - lots of different people, ones who I hadn't grown up with, and who didn't listen to her. I'll never know why she took such a dislike to me almost from the day I started school, but she caused a lot of damage - I'm a lot more confident these days but have a terrible fear of rejection, e.g. I'd never throw a party, or ask a group of people round.
Try and foster friendships outside of school - not easy at the moment, but things like craft clubs, brownies or scouts, swimming lessons, other sports - maybe with people she doesn't go to school with.