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A bunch of people, whether they are the most or the least, all banded together by some stupid reason, like being mad at someone else or wanting more stuff, even if it means screwing others over.
My whole class is a faction because they all hate the teacher and keep giving her bad vibes.
The football team is a faction because they think they're the best and everyone else is trash.
My mom and her friends are a faction because they all think they're the most important people in the world.