I tortured a kid or two in my youth. Was explosively violent like that (kicked a couple kids bad enough to make them cry), was downright mean, non-trusting of 99% of the people I came in contact with especially my peers. If you can afford it, I suggest getting her a little extra help learning how to identify and deal with her anger.
I got worse at about age 10. You probably know me well enough to know some of the issues I've had as an adult, especially with my anger. I can't tell you WHY I'm this way but I can tell you (1) I am SO glad you got her away from her alcoholic mother and (2) If I had had help when I was younger, I wonder if life would have been easier?
Talk to her about what happened, talk to her about the group therapy and how that is going, talk to her about when YOU get angry, but do it as a share. Let the school dole out the punishment but don't turn your back on the issue please. Might help to use this as an opportunity to turn LMC on to Higher Power. What about the story of Job? Do you have a kid's book of bible stories. (Assuming you are still doing the church thing). You can talk to her about right and wrong. Nobody ever told me it was wrong to kick someone in the face. Maybe I should have known, but sorry, I didn't. I wish somebody had told me.
Thank you for asking my opinion. Thank you for posting and sharing and being open-minded for LMC's well-being.