Janko groups

The Janko groups denoted by $J_1,J_2,J_3$, and $J_4$ are four of the 26 sporadic groups. They were discovered by . Janko in 1966 and published in the article ”A new finite simple group with abelian Sylow $2$-subgroups and its characterization.” (Journal of Algebra, 3, 1966, 32: 147-186).

Each of these groups have very intricate matrix representations as maps into large general linear groups. For example, the matrix $K$ corresponding to $J_4$ gives a representation of $J_4$ in $G{L}_{112}(2)$.

Title	Janko groups
Canonical name	JankoGroups
Date of creation	2013-03-22 13:59:17
Last modified on	2013-03-22 13:59:17
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	12
Author	mathcam (2727)
Entry type	Definition
Classification	msc 20D08
Related topic	ExamplesOfFiniteSimpleGroups
Related topic	Solvable