Mathieu group

The list

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	Prime factorization of order	Number of conjugacy classes	Sporadic simple?	Simple?	Almost simple?	Alternative descriptions
9	Mathieu group:M9	72	$2^{3}\cdot 3^{2}$	6	No	No	No	projective special unitary group $PSU(3,2)$
10	Mathieu group:M10	720	$2^{4}\cdot 3^{2}\cdot 5$	8	No	No	Yes	?
11	Mathieu group:M11	7920	$2^{4}\cdot 3^{2}\cdot 5\cdot 11$	10	Yes	Yes	Yes	--
12	Mathieu group:M12	95040	$2^{6}\cdot 3^{3}\cdot 5\cdot 11$	15	Yes	Yes	Yes	--
21	Mathieu group:M21	20160	$2^{6}\cdot 3^{2}\cdot 5\cdot 7$	10	No	Yes	Yes	projective special linear group $PSL(3,4)$
22	Mathieu group:M22	443520	$2^{7}\cdot 3^{2}\cdot 5\cdot 7\cdot 11$	12	Yes	Yes	Yes	--
23	Mathieu group:M23	10200960	$2^{7}\cdot 3^{2}\cdot 5\cdot 7\cdot 11\cdot 23$	17	Yes	Yes	Yes	--
24	Mathieu group:M24	244823040	$2^{10}\cdot 3^{3}\cdot 5\cdot 7\cdot 11\cdot 23$	26	Yes	Yes	Yes	--