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Janko Group J2

The Janko group J_2, also known as the Hall-Janko group HJ, is one of the four Janko groups. It is a sporadic group and simple group of group order 604800=2^7·3^3·5^2·7 (Conway et al. 1985).

The group J_2 acts on the Hall-Janko graph and the Hall-Janko near octagon. In each case, its action realizes it as a subgroup of the full automorphism group (Hall and Wales 1968, Brouwer et al. 1989). The full groups are both denoted J_2.2 and have group order 1209600 (DistanceRegular.org). Thus J_2, of group order 604800, has index 2 in each full group.

The group is implemented in the Wolfram Language as JankoGroupJ2[].

See also

Hall-Janko Graph, Hall-Janko Near Octagon, Janko Groups, Simple Group, Sporadic Group

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References

Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. Distance Regular Graphs. New York: Springer-Verlag, pp. 408-410, 1989.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.DistanceRegular.org. "Hall-Janko Graph." https://www.math.mun.ca/distanceregular/graphs/halljanko.html.DistanceRegular.org. "Hall-Janko Near Octagon from J_2.2 = Cohen-Tits Near Octagon." https://www.math.mun.ca/distanceregular/graphs/halljanko315.html.Hall, M. Jr. and Wales, D. "The Simple Group of Order 604,800." J. Algebra 9, 417-450, 1968.Wilson, R. A.; Parker, R. A.; and Bray, J. N. "ATLAS: Janko Group J_2." https://brauer.maths.qmul.ac.uk/Atlas/spor/J2/.

Referenced on Wolfram|Alpha

Janko Group J2

Cite this as:

Weisstein, Eric W. "Janko Group J2." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/JankoGroupJ2.html

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