Mathieu group:M22

From Groupprops
Jump to: navigation, search
This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this group
View a complete list of particular groups (this is a very huge list!)[SHOW MORE]


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