Faction rhymes with:
dissatisfaction, liquefaction, satisfaction, abstraction, action, attraction, classaction, contraction, diffraction, dissatisfaction, distraction, exaction, extraction, fraction, inaction, infraction, interaction, liquefaction, reaction, retraction, satisfaction, subtraction, telaction, traction, transaction
Faction sounds like:
facedown, fasten, faustian, faustina, faustine, faustino, festoon, fiction, fightin', fixation, fochtman, fuston