Higman-Sims group

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Definition

This group, denoted HS, and termed the Higman-Sims group, is one of the sporadic simple groups and was discovered by Higman and Sims. It has order:

$\!44352000=2^{9}\cdot 3^{2}\cdot 5^{3}\cdot 7\cdot 11$

Arithmetic functions

Function	Value	Similar groups	Explanation
order (number of elements, equivalently, cardinality or size of underlying set)	44352000	groups with same order

Arithmetic functions of a counting nature

Function	Value	Explanation
number of conjugacy classes	24

Group properties

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