She is not wanting a solution. She wants to vent. So just listen and let her know you care about how she feels. Be empathetic.
If she's doing this for sympathy, it shows she needs sympathy. She needs you to understand/accept that she's having a difficult time. She needs reassurance that you love her enough to just listen. I suggest that sometimes you reflect her feelings back to her by saying such things as, "I know you're having a rough time." My adult daughter and teen grandchild hate for me to ask questions while they're venting. They don't want a solution. I try to just listen. It's hard to do the first few times. I'm finally able to just listen without making an comments.
I suggest you set a boundary that helps you. Such as I'll listen for 10 minutes and after that we'll talk about something else. After school is common time for decompressing. She's a teen. Drama is to be expected.
She keeps repeating her complaints because she doesn't feel heard. I suggest that if you can be a compassionate listener some of the time she will complain less.
I've learned to only listen with a few ums and ohs, letting her know you've heard. I remain emotionally unconnected. Parents are not responsible to change the way kids feel. I suggest you just accept that she feels this way at the moment.
I urge you to read How To Listen so Kids Will Talk by Adele Faber. There is one focused on teens.
I suggest that her unhappiness is in part caused by her not having friends. She is complaining to you because she doesn't have the outlet of complaining with friends. I suggest finding a way to help her make friends. Is she involved in school related clubs or sports? What are her interests?. Perhaps you could encourage her get involved. Perhaps invite a classmate to have a "playdate" after school. Perhaps have her invite someone to see a movie with her. Perhaps take a friend for a snack after school. Encourage her to invite someone she'd like to be friends with.