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This group, denoted , and also called the Hall-Janko group and sometimes denoted , 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:
It is one of the sporadic simple groups.
|order (number of elements, equivalently, cardinality or size of underlying set)||604800||groups with same order|
Arithmetic functions of a counting nature
|number of conjugacy classes||21||See element structure of Janko group:J2|
|simple group, simple non-abelian group||Yes|
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: