Mathieu group
In
mathematics, the
Mathieu groups were the first known sporadic groups. The largest of them, M
24, is the
automorphism group of the
binary Golay code, i.e., the group of permutations of coordinates mapping
W to itself. We can also regard it as the intersection of S
24 and Stab(
W) in Aut(
V). This is a finite
simple group. The simple subgroups M
23, M
22, M
12, and M
11 can be defined as the stabilizers in M
24 of a single coordinate, an ordered pair of coordinates, a 12-element subset of the coordinates corresponding to a code word, and a 12-element code word together with a single coordinate, respectively.
References
- Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; Wilson, R. A. (1985). Atlas of finite groups. Maximal subgroups and ordinary characters for simple groups. With computational assistance from J. G. Thackray. Eynsham: Oxford University Press. ISBN 0-19-853199-0