Gladiator Factions?

Were there factions among gladiators and their schools  that would be akin to the chariot races?

If not were there any famous historical gladiator schools or owners outside the 4 they name in Rome (magnus, dacicus, Gallic, and Matutinus)?

any names or references is much appreciated.

No, no factions. In fact the ownership of specific gladiators wasn't important to the public, they were only interested in a thrilling fight and a pile of coins from their betting. As for the gladiators themselves, they were generally intensely loyal to their owners and part of his familia, the brotherhood of gladiators that he owned. 

Owners varied. Cicero for instance praises the fighters owned by his friend Atticus in a letter and tells him that if he had rented them out, he would have easily recovered his expenses in the last two events. For Atticus, it was a hobby.

There were two centres of gladiator schooling. The four major ones in Rome probably held as many as two thousand gladiators, and there were other large schools in Capua, Campania, not far from Pompeii. Smaller schools might exist in any Roman city or its environs. Pompeii for instance had a gladiator barracks

Recently another was found in Austria and the artists impression shows the training arena that the large schools always used...