Conway group:Co1

Definition
The group, denoted $$\operatorname{Co}_1$$, is defined as the inner automorphism group of $$\operatorname{Co}_0$$ (see defining ingredient::Conway group:Co0), which in turn is defined as the automorphism group of the defining ingredient::Leech lattice.

Note that $$\operatorname{Co}_0$$ has a center which is isomorphic to cyclic group:Z2, with the non-identity element corresponding to the automorphism given by sending every vector to its negative. Thus, $$\operatorname{Co}_1$$ is the quotient group of $$\operatorname{Co}_0$$ by a subgroup of order two.

The group is a finite simple non-abelian group, and in fact, it is one of the 26 sporadic simple groups. It is also one of the three defining ingredient::Conway groups.