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The Automorphism Group 
 of the Leech Lattice modulo a center of order two is called ``the''
Conway group.  There are 15 exceptional Conjugacy Classes of the Conway group. This group,
combined with the Groups 
 and 
 obtained similarly from the Leech Lattice by
stabilization of the 1-D and 2-D sublattices, are collectively called Conway groups.  The Conway groups are
Sporadic Groups.
See also Leech Lattice, Sporadic Group
References
Wilson, R. A.  ``ATLAS of Finite Group Representation.''
http://for.mat.bham.ac.uk/atlas/html/contents.html#spo.