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Janko Groups

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The Janko groups are the four sporadic groups J_1, J_2, J_3 and J_4. The Janko group J_2 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 summarized the group orders of the Janko groups.

grouporderfactorization
J_11755602^3·3·5·7·11·19
J_26048002^7·3^3·5^2·7
J_3502329602^7·3^5·5·17·19
J_4867755710460775628802^(21)·3^3·5·7·11^3·23·29·31·37·43

See also

Livingstone Graph, Sporadic Group

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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_4." J. Algebra 219, 113-172, 1999.Wilson, R. A. "ATLAS of Finite Group Representation." http://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 Web Resource. https://mathworld.wolfram.com/JankoGroups.html

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