Conway group:Co2

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Definition

This group, denoted ${\mathrm{C}}_{\mathrm{o}}$, 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 ${\mathrm{C}}_{\mathrm{o}}$ trivially, it can be realized as a subgroup of Conway group:Co1, the inner automorphism group of ${\mathrm{C}}_{\mathrm{o}}$.

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.