Mathieu group:M23

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VIEW DEFINITIONS USING THIS AS EXAMPLE: All terms |Group properties |Subgroup properties|
VIEW FACTS USING THIS AS EXAMPLE: All facts |Group property non-implications |Subgroup property non-implications |Group metaproperty dissatisfactionsSubgroup metaproperty dissatisfactions

Definition

This is the Mathieu group of degree 23, denoted $M_{23}$, and is the subgroup of the symmetric group of degree 24 generated by the following permutations:

$M_{23}:=⟨(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23),(3,17,10,7,9)(4,13,14,19,5)(8,18,11,12,23)(15,20,22,21,16)⟩$

Arithmetic functions

Function	Value	Similar groups	Explanation
order (number of elements, equivalently, cardinality or size of underlying set)	10200960	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	17

Group properties

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

GAP implementation

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

Description	Functions used
MathieuGroup(23)	MathieuGroup