Janko group:J4

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Definition

This group, denoted $J_{4}$, is one of the Janko groups. Its existence was conjectured by Janko.

The order of the group is:

$\!86775571046077562880=2^{21}\cdot 3^{3}\cdot 5\cdot 7\cdot 11^{3}\cdot 23\cdot 29\cdot 31\cdot 37\cdot 4$

Arithmetic functions

Function	Value	Similar groups	Explanation
order (number of elements, equivalently, cardinality or size of underlying set)	86775571046077562880	groups with same order

Arithmetic functions of a counting nature

Function	Value	Explanation
number of conjugacy classes	62	See element structure of Janko group:J4