Mathieu group:M24
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Definition
This is the Mathieu group of degree 24, denoted , and is the subgroup of the symmetric group of degree 24 generated by the following permutations:
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 |