Conway group:Co2

This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this group
View a complete list of particular groups (this is a very huge list!)[SHOW MORE]

VIEW FACTS ABOUT THIS GROUP: All factsGroup property satisfactionsSubgroup property satisfactionsGroup property dissatisfactionsSubgroup property satisfactions
VIEW DEFINITIONS USING THIS AS EXAMPLE: All terms |Group properties |Subgroup properties|
VIEW FACTS USING THIS AS EXAMPLE: All facts |Group property non-implications |Subgroup property non-implications |Group metaproperty dissatisfactionsSubgroup metaproperty dissatisfactions

Definition

This group, denoted $\operatorname {Co} _{2}$, is defined as the subgroup of Conway group:Co0 (the automorphism group of the Leech lattice) that is the isotropy subgroup of the nonzero vector of length 4 in the lattice.

Since the subgroup intersects the center of $\operatorname {Co} _{0}$ trivially, it can be realized as a subgroup of Conway group:Co1, the inner automorphism group of $\operatorname {Co} _{0}$.

The group is a finite simple non-abelian group. In fact, it is one of the 26 sporadic simple groups and one of the three Conway groups.