Conway group:Co3

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Definition

This group, denoted $\operatorname{Co}_3$, is defined as the subgroup of Conway group:Co0 (the automorphism group of the Leech lattice) comprising the automorphisms that fix a particular vector of length 6, i.e., the isotropy subgroup of length 6.

Since the subgroup intersects the center of Conway group:Co0 trivially, it can also be viewed as a subgroup of Conway group:Co1, which is the inner automorphism group of the Conway group:Co0.

This is a finite simple non-abelian group that is one of the 26 sporadic simple groups, and is also one of the three Conway groups.