Janko group:J2

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This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this group
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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 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