Janko group

In mathematics, the Janko groups J₁, J₂, J₃ and J₄ are four of the twenty-six sporadic groups; their orderss are 2³.3.5.7.11.19 (J₁), 2⁷.3³.5².7 (J₂), 2⁷.3⁵.5.17.19 (J₃) and 2²¹.3³.5.7.11³.23.29.31.37.43 (J₄), respectively.

The Janko groups were first described by mathematician Zvonimir Janko in 1966; each of these groups has intricate matrix representationss as mapss into large general linear groups. For example, the matrix corresponding to J₄ gives a representation of J₄ in GL(112, 2).

External links

• PlanetMath: Janko groups
• Atlas of Finite Group Representations: J₁
• Atlas of Finite Group Representations: J₂
• Atlas of Finite Group Representations: J₃
• Atlas of Finite Group Representations: J₄

References

• Zvonimir Janko, A new finite simple group with abelian Sylow subgroups and its characterization, Journal of Algebra 32:147-186, 1966