Mathieu group:M22

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Definition

This is the Mathieu group of degree 22, denoted M_{22}, and is the subgroup of the symmetric group of degree 22 generated by the following permutations:

M_{22} := \langle  (1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22), (1,4,5,9,3)(2,8,10,7,6)(12,15,16,20,14)(13,19,21,18,17), (1,21)(2,10,8,6)(3,13,4,17)(5,19,9,18)(11,22)(12,14,16,20) \rangle

Arithmetic functions

Function Value Similar groups Explanation
order (number of elements, equivalently, cardinality or size of underlying set) 443520 groups with same order
exponent of a group 9240 groups with same order and exponent of a group | groups with same exponent of a group


Arithmetic functions of a counting nature

Function Value Explanation
number of conjugacy classes 12

Group properties

Property Satisfied? Explanation
abelian group No
nilpotent group No
solvable group No
simple group Yes
minimal simple group No

GAP implementation

GAP's SmallGroup library is not available for this large order.

Description Functions used
MathieuGroup(22) MathieuGroup