So, I have five main characters, and one of them starts out pretty mean. She's friends with a lot of snobby people, and while she doesn’t set out to maliciously attack anyone, she doesn’t stand against it either. For example, she won’t start making fun the school outcast, but she will join in if her group of friends do. Of course she's supposed to have a redemption story and won't stay like this for the whole thing, but I don't think it's a good idea since people like characters that are, well, likeable. I want her to be mean, but not to the point where people can't stand her and wish for her death (I've seen people do that in reviews for books featuring a similar character). And I intend to make her more likeable down the line, but I feel people won't forgive her or ever grow to like her. I made her because I wanted my characters to have interesting story arcs and I didn't want to do another 'nice and shy' girl, but I don't know if it'll work out.
If you're going with the standard Five Man Band trope, then it's pretty much a given that you have an snarky, kinda mean, anti-hero type to act as a foil for the leader.
If you want the readers to feel for her from the start, you could show her motivations (whether she is fully aware of them or not) for acting like a mean girl. If you want her to become likable only later on in the story, you could still show early on that she is redeemable, perhaps by having her do a kind gesture when no one's watching.
Hving a mean girl as a main character is not necessarily a bad thing, specially considering you want her to get a redemption arc. Maybe you should consider that most real life mean girls, won't bully you just for the sake of it. Based on my own life experience I can say one thing: They don't do it just because they are mean, at least most of them don't. I am going to share with you a bit of my experience as being a "mean girl" and maybe give you an insight into why I did the things I did. I actually was a part of the "mean girls" at my school when I was in middle school and even though I stopped hanging out with them, and actually started hanging out with a bunch of outcasts, I still was friends with them for a while. It is very weird, because when you are the one doing this sort of thing, sometimes you don't realize you are being mean. I wouldn't have classified myself as a mean girl at that point in my life... But when I look back at the way we acted and treated other people I see more and more clearly that we weren't being nice at all. Of course, it wasn't like in the movies where we were a group of popular girls, who liked to shit on others, but we did gossip a lot and say mean things to some poor girls that were just a bit different. And there were times I wanted to disagree but the social pressure that came with being one of them was massive, I was always afraid I would loose their friendship if I didn't agree with them... and at that point they were my only friends... It came to a point in which what they liked became what I liked, and I would keep certain things that I liked in secret, afraid they would judge me for it. If you don't want to go to the social pressure route, you can always find another reason, I've seen girls who bully others because of envy or because they feel bad about themselves. A friend of mine even convinced me I was ugly and that I would never have a boyfriend or have a guy like me just because she couldn't stand the fact that I was smart and not ugly (I won't say I am pretty, but I am not ugly either...). These were my experiences with being friends with mean girls, but I believe there are countless other reasons to why a girl would bully others... I think in your case the social pressure may work because like you said she is not mean on her own but only around her friends, what looks a lot like what I did in the past. I think as long as you give her a clear reason to do what she does (even if it is not a good excuse and in real life we would dislike her) she will feel more real and easier to relate to. OBS: Sorry for my english I am foreign so sometimes I may commit very weird grammar mistakes or not express myself clearly.
The other four viewpoints might help balance out the tone. With readers, especially in a book where there is a group of characters, they're always going to hate on someone. I don't think anyone ever gushes over every character. I remember reading the Babysitter's Club series back in the 80s and nobody could stand their 'leader' of the group Kristy because she was just so bossy. Meanwhile we kept on reading the series. Don't try to please your intended audience too much. They're very contradictory. Write what you like -- that will shine through more and if you do it with confidence and unapologetically it will benefit your writing. Also have a sense of humor about it. Sometimes the bad girls can be funny.
I think it should be okay. You said she's going to have a redemptive character arc, so it's not like it's going she's going to be a complete antagonist. And you have other main characters to focus on as well. Readers may see her as a really different voice in the group, and they might even appreciate that a little.
I never understood the "likeable characters" thing. People are flawed and don't always do the right thing, and characters should be that way too. My advice: make sure the character is interesting. A lot of times, these unlikeable characters don't get a past, not so much because they are "unlikeable" bt because they are uninteresting, and readers don't have a reason to care about them or what is going on in their lives. Ask yourself what it is about this character that people will want to read about. What does she do? What does she think? What is her life like that people want to be invested in her? What does she believe and why does she believe? Also, ask yourself what your goal is for this story. If the whole goal is to root for the character, then having an unlikeable character may not be your best bet, but based off what you've written here, I'm going to assume the goal for your story is to show the changes that people go through in life, and maybe a few lessons, not just for the character, but for the reader as well. But ask yourself it is you want for this story and whether or not this sort of character is the best for executing it.
Not a book but Happy Death Day started with a completely unlikable character. Her redemption was so well done you couldn't help but fall for her in the end. I don't think it's bad to have your characters start out mean.
Make her mean, but show her vulnerable side. That way your audience immediately has a reason to sympathize with her. The vulnerability should also inform her nasty attitude as well.
Everyone else has already given great advice, but just to add in my two cents: Being a “mean girl” isn’t the only thing that makes her who she is. Just like having anxiety or liking a certain thing or disliking another or being part of a different ethnicity than lots of others doesn’t make up the totality of who someone is. Give her personality, give her fears and dreams, vulnerability and bravery. As @Odile_Blud said, “likable characters” aren’t nesscesarily good. Give her flaws, thereby giving the reader a relatable character, which will most likely allow them to sympathize with her more than just being “friendly” or “nice” will. Personally I’d enjoying reading the perspective of a “mean girl”. Good luck writing!
Although not as similar, another unlikable but then overtime becomes a better character is Steve Harrington from Stranger Things. Like your mean girl character, he starts out being the cool guy, doing risky thinks and treating everyone not as popular with disdain. Throughout the series he becomes less of the that "cool person" stereotype and more of a hero. Also, in my opinion, your mean girl to redemptive girl character arc is a great idea, and if I were you I would not worry about the likability of the character. Readers will start to sympathize and relate to her when she goes through her redemptive character arc throughout the story.
Also keep in mind that your readers will have very individual reactions to this. If you do a really believable 'mean girl', probably a lot of your readers will be reminded of their own school years, and their reactions will be coloured by how they felt about the 'mean girls' they knew growing up. If you trigger really bad memories in a reader, then it's possible no amount of complex and sympathetic characterization will get them to like that girl, because there's just too much hurt behind their reaction.
