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This group, denoted , 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 trivially, it can be realized as a subgroup of Conway group:Co1, the inner automorphism group of .
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.