Max is a young tomcat with deep blue eyes and a multicolor pelt with a number of ticks (often causing the young cat to scratch his pelt to get rid of them). He lives with an human physicist.
Francis meets Max in the novel Gottergleicht when, after being captured by the Brotherhood of the Black, the younger cat is going to be a lawyer for Francis, and informs the detective that that he's going to persuade the jury of black cats that Francis is not going to publicly disclose what was happening.
Max fails to convince Francis to be collaborative, but the protagonist is saved by the same time running-back event before the black cats can carry out the sentence on him.
Later Francis will investigate into the Max's home to search clues about the Brotherhood of the Black: he will found that Max's human master is a physicist, an acquaintance of his own master Gustav. Francis thinks that's because the Max's master activity, the younger cat learned of the time-back running event.
Max is found killed into his home and it's soon revealed that the murderer was Bluebeard that's then killed after clashing with Francis: this events however are soon canceled by the time running-back event. (the Brotherhood created this new alternate time, where they had included Bluebeard among their ranks, to eliminate the possibility that Francis could gain clues from Max).
It's unclear if Max is actually a member of the Brotherhood of Black (that seems to include also normal not-black cats), and its efforts as lawyers seems to be directed to make the upheaval for the feline population the less shocking and dangerous. (However it's not told that he was aware of the true nature of the Brotherhood and it's also possible that he wanted simply to save the life of the cats indicted).
With the conclusion of the book, it's said that all the cats forget the whole adventure, it's likely that Max (whose death is a never-happened event) kept on his previous life with his human master.