# Conway group:Co2

## 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.