The Janko groups are the four sporadic groups J1, J2,
J3, and J4.
The Janko group J2 is also known
as the Hall-Janko group.
The Janko groups are implemented in the Wolfram Language as JankoGroupJ1[],
JankoGroupJ2[],
JankoGroupJ3[],
and JankoGroupJ4[].
The following table summarizes the group orders of
the Janko groups.
| group | order | factorization |
| J1 | 175560 |  |
| J2 | 604800 |  |
| J3 | 50232960 |  |
| J4 | 86775571046077562880 |  |
See also
Hall-Janko Graph,
Hall-Janko Near Octagon,
Janko Group J1,
Janko
Group J2,
Janko Group J3,
Janko
Group J4,
Livingstone Graph,
Sporadic
Group
Explore with Wolfram|Alpha
References
Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A. Atlas
of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups.
Oxford, England: Clarendon Press, 1985.Ivanov, A. A. and Meierfrankenfeld,
U. "A Computer-Free Construction of 
." J. Algebra 219, 113-172, 1999.Wilson,
R. A. "ATLAS of Finite Group Representation." https://brauer.maths.qmul.ac.uk/Atlas/v3/spor/.Referenced
on Wolfram|Alpha
Janko Groups
Cite this as:
Weisstein, Eric W. "Janko Groups." From
MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/JankoGroups.html
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