Mult = 1.

Out = 1.

< *a*, *b* | *a*^{2} = *b*^{5} = (*ab*)^{17} = [*a*, *b*]^{3} = [*a*, *b*^{2}]^{4} = [*a*, *bab*]^{3} = [*a*, *b*^{2}*abab*^{2}]^{2} = [*a*, *b*^{2}*ab*^{2}]^{3} = [*a*, (*ab*^{2})^{4}]^{2} = [*a*, *babab*]^{3} = (*ababab*^{2}*ab*^{-1}*ab*^{-2})^{4} = 1 >.

Degree | Type/Ring | Generators | Name | Info | Comments (if any) | ||
---|---|---|---|---|---|---|---|

Permutation representations | |||||||

120 | permutation | a |
b |
S82p120 | - | 2-transitive (in fact, 2-primitive) | |

136 | permutation | a |
b |
S82p136 | - | 2-transitive (in fact, 2-primitive) | |

240 | permutation | a |
b |
S82p240 | - | imprimitive | |

255 | permutation | a |
b |
S82p255 | - | - | |

272 | permutation | a |
b |
S82p272 | - | imprimitive | |

2295 | permutation | a |
b |
S82p2295 | - | - | |

5355 | permutation | a |
b |
S82p5355 | - | - | |

Faithful irreducibles in characteristic 2 | |||||||

8 | GF(2) | a |
b |
S82f2r8 | - | The natural representation | |

16 | GF(2) | a |
b |
S82f2r16 | - | - | |

26 | GF(2) | a |
b |
S82f2r26 | - | - | |

48 | GF(2) | a |
b |
S82f2r48 | - | - | |

Faithful irreducibles in characteristic 3 | |||||||

35 | GF(3) | a |
b |
S82f3r35 | - | - | |

50 | GF(3) | a |
b |
S82f3r50 | - | - | |

Faithful irreducibles in characteristic 5 | |||||||

35 | GF(5) | a |
b |
S82f5r35 | - | - | |

51 | GF(5) | a |
b |
S82f5r51 | - | - | |

Faithful irreducibles in characteristic 7 | |||||||

35 | GF(7) | a |
b |
S82f7r35 | - | - | |

51 | GF(7) | a |
b |
S82f7r51 | - | - | |

Faithful irreducibles in characteristic 17 | |||||||

35 | GF(17) | a |
b |
S82f17r35 | - | - | |

51 | GF(17) | a |
b |
S82f17r51 | - | - | |

Faithful irreducible in characteristic 0 | |||||||

35 | Z |
a and b |
S82Zr35 | - | - |

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Last updated 7th December 1998,

R.A.Wilson, R.A.Parker and J.N.Bray