# 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^{} |