# 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")