This is for the CSA (and, by extension, Zsinj). Neither would be part of the Pentastar Alignment or any other faction, and Hutt ships wouldn't have been used by the CSA. The reasoning for the Lucrehulk was they bought out a ton of the old CIS/Republic hardware, even if the Lucrehulk isn't reallu explicitly one of the things they're mentioned as having used. The reasoning for the Invincible is that poretty much any time you see the CSA mentioned, the Invincible is part of that somewhere, and any time you see the Invincible mentioned, the CSA is part of it somewhere.
In 18 BBY a union of pirates were launching raids into the recently reorganized CorpSec and the surrounding area, that forced the Empire to get involved in what was known as the Listehol Campaign. Admiral Wullf Yularen took command of a group of Invincible-class Dreadnaughts meant for the CSA and a small complement of Venators and TIE/LN starfighters, quickly defeating the raiders. - Essential Guide to Warfare.
Lt. Comm Angela Krin, who's a CSA and Zsinj hero, also used an Invincible and also has demonstrated a propensity for standing in front of them:
http://starwars.wikia.com/wiki/Angela_Krinhttp://starwars.wikia.com/wiki/Resolute_(Invincible-class)
