The correct answer is: " a group that strongly disagrees with another group."
Usually, a faction is a term mostly used in politics to refer to a group, which comprises a minority within a larger organization, for example a goverment, a political party, or a trade union, and it starts to dissent with the rest of the group. The faction starts to develop a political purpouse that is different to the one of the rest of the entity.
African Americans who served in the Civil war were treated with inadequate weapons and medical treatments. Though they were treated differently than white people, they were still treated better in the military.