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Groupprops β

Higman-Sims group

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