The Mystery of Magic, also known as the Mystery of Mogic and the Misery of Magic, is a mysterious group of bureaucratic wizards who appear to be based on the Ministry of Magic from the books. They seem to hold a lot of power over Hogwards, and are able to send anyone they want to random places in the Caucasus. (Examples of this are Azerbaijan and Abkhazia, which is probably meant to be Azkaban)
The Mystery of Magic first appears in Chapter 21. The bureaucrats from the Mystery want Hogwarts closed. Cornelia Fuck points out that the "BARK LORD" is planning to kill the students. Doris Rumbridge points out that Dumblydore is unfit to be principal, that his Alzheimer's is dangerous, and that he should "retry".
Later in the story, Cornelio Fuck arrives at the school. Fuck takes over teaching Potions once Snap is sent to prison. Fuck tells Draco that Dumblydore has been imprisoned due to him being "week" and having "kancer." Rumbridge also comes back to the school; she informs the students that Professor Sinister has been sent to Azerbaijan for being "too gottik."
Unlike most factions, it is not outwardly stated whether the Mystery of Magic aligns more with the "Goffs" or the "Preps", though due to the dress of known members and the fact Professor Sinister was arrested for being "too gottik", it seems likely they are fairly preppy.