'Each other' refers to a reciprocal action: I do X to you and you do X to me; we do X to each other. 'Together' refers to a common action: You and I do X to someone or something else; we do X together.
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You Can say stop hitting each other but you Can not say stop hitting together . I guess you use together when you do something together with somebody else & each other when you do something to each other , where you alone are doing something but that other person do it back to you