Mathieu group:M24

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Definition

This is the Mathieu group of degree 24, denoted $M_{24}$, and is the subgroup of the symmetric group of degree 24 generated by the following permutations: $M_{24} := \langle (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23), (3,17,10,7,9)(4,13,14,19,5)(8,18,11,12,23)(15,20,22,21,16), (1,24)(2,23)(3,12)(4,16)(5,18)(6,10)(7,20)(8,14)(9,21)(11,17)(13,22)(15,19) \rangle$

Arithmetic functions

Function Value Similar groups Explanation
order (number of elements, equivalently, cardinality or size of underlying set) 244823040 groups with same order
exponent of a group 212520 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 26

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(24) MathieuGroup