noun /ˈfæk.ʃən,ˈfæk.ʃn/
a) A group of people, especially within a political organization, who express a shared belief or opinion different from people who are not part of the group.
Publick [sic] affairs soon fell into the utmost confusion, and in this state of faction and perplexity, the island continued, until its re-capture by the French in 1779.
b) Strife; discord.
He asks the audience if they believe that they will be more loved by the gods if the city is in a state of faction than if they govern the city with good order and concord.
Wikipedia foundation.