Monster Group - McKay's E₈ Observation

McKay's E₈ Observation

There are also connections between the monster and the extended Dynkin diagrams specifically between the nodes of the diagram and certain conjugacy classes in the monster, known as McKay's E₈ observation. This is then extended to a relation between the extended diagrams and the groups 3.Fi₂₄', 2.B, and M, where these are (3/2/1-fold central extensions) of the Fischer group, baby monster group, and monster. These are the sporadic groups associated with centralizers of elements of type 1A, 2A, and 3A in the monster, and the order of the extension corresponds to the symmetries of the diagram. See ADE classification: trinities for further connections (of McKay correspondence type), including (for the monster) with the rather small simple group PSL(2,11) and with the 120 tritangent planes of a canonic sextic curve of genus 4.