Editing Monster group (section)

== McKay's E<sub>8</sub> observation ==
There are also connections between the monster and the extended [[Dynkin diagram]]s <math>\tilde E_8</math> specifically between the nodes of the diagram and certain conjugacy classes in the monster, known as ''McKay's E<sub>8</sub> observation''.{{sfn|Duncan|2008}}{{sfn|le Bruyn|2009}}{{sfn|He|McKay|2015}} This is then extended to a relation between the extended diagrams <math>\tilde E_6, \tilde E_7, \tilde E_8</math> and the groups 3.Fi<sub>24</sub>{{prime}}, 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 group]]s 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|ADE classification: trinities]] for further connections (of [[McKay correspondence]] type), including (for the monster) with the rather small simple group [[projective special linear group|PSL]](2,11) and with the 120 tritangent planes of a canonic sextic curve of genus 4 known as [[Bring's curve]].