Conway group:Co2

Definition
This group, denoted $$\operatorname{Co}_2$$, is defined as the subgroup of defining ingredient::Conway group:Co0 (the automorphism group of the defining ingredient::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 defining ingredient::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 defining ingredient::Conway groups.