# 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 $GL_{112}(2)$.

Title Janko groups JankoGroups 2013-03-22 13:59:17 2013-03-22 13:59:17 mathcam (2727) mathcam (2727) 12 mathcam (2727) Definition msc 20D08 ExamplesOfFiniteSimpleGroups Solvable