Janko group:J2

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Definition

This group, denoted $J_{2}$, and also called the Hall-Janko group and sometimes denoted $HJ$, is one of the Janko groups. Its existence was conjectured by Zvonimir Janko and it was constructed by Hall and Wales.

The order of the group is:

$\!604800=2^{7}\cdot 3^{3}\cdot 5^{2}\cdot 7$

It is one of the sporadic simple groups.

Arithmetic functions

Function	Value	Similar groups	Explanation
order (number of elements, equivalently, cardinality or size of underlying set)	604800	groups with same order

Arithmetic functions of a counting nature

Function	Value	Explanation
number of conjugacy classes	21	See element structure of Janko group:J2

Group properties

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

GAP implementation

GAP does not have an implementation of this group as a group. However, the character table of the group can be accessed as a stored table using GAP's CharacterTable function, if the CtblLib package is loaded:

CharacterTable("J2")

External links

• J2 on the Atlas of Finite Groups