Interfaction looks like it means between-factions, in fact I could swear I've seen it used like that... anyway, it looks to me like it would be describing some sort of civil unrest (interfactional fighting broke out in <country> today...) or bureaucratic nonsense in a company (BigSoftwareCompany was unable to respond to their upstart rivals due to interfactional disagreements about which pointy haired boss would get more seats to fill). Neither is really badass -- the latter is mostly tedious, the former is often horrifying.