Element structure of Mathieu groups

From Groupprops

This article gives specific information, namely, element structure, about a family of groups, namely: Mathieu group.
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Particular cases

There are eight isomorphism classes of Mathieu groups, given by their degrees. The degree of a Mathieu group is the smallest size set on which it has a faithful permutation representation, which is precisely the representation of interest:

Degree Mathieu group Order of group Sporadic simple? Simple? Almost simple? Element structure page
9 Mathieu group:M9 72 No No No element structure of Mathieu group:M9
10 Mathieu group:M10 720 No No Yes element structure of Mathieu group:M10
11 Mathieu group:M11 7920 Yes Yes Yes element structure of Mathieu group:M11
12 Mathieu group:M12 95040 Yes Yes Yes element structure of Mathieu group:M12
21 projective special linear group:PSL(3,4) 20160 No Yes Yes element structure of projective special linear group:PSL(3,4)
22 Mathieu group:M22 443520 Yes Yes Yes element structure of Mathieu group:M22
23 Mathieu group:M23 10200960 Yes Yes Yes element structure of Mathieu group:M23
24 Mathieu group:M24 244823040 Yes Yes Yes element structure of Mathieu group:M24