Artin representations were computed with Magma by Tim Dokchitser and John Jones.

Bounds for completeness of computations come from [MR:3669395, 10.1007/s40993-017-0079-5, arXiv:1610.01228] . In each case, the LMFDB contains all faithful representations for a given group and irreducible representation with conductor less than or equal to the stated bound. Representations are distinguished by their dimension, and the smallest containing permutation representation.

Group | Dim | Container | Bound |
---|---|---|---|

$C_2$ | 1 | 2T1 | 10000 |

$C_3$ | 1 | 3T1 | 11180 |

$C_4$ | 1 | 4T1 | 796 |

$C_5$ | 1 | 5T1 | 752 |

$C_6$ | 1 | 6T1 | 577 |

$S_3$ | 2 | 3T2 | 177662241 |

$C_7$ | 1 | 7T1 | 483 |

$C_8$ | 1 | 8T1 | 249 |

$D_4$ | 2 | 4T2 | 22500 |

$Q_8$ | 2 | 8T5 | 215444 |

$C_9$ | 1 | 9T1 | 387 |

$D_{5}$ | 2 | 5T2 | 40000 |

$A_{4}$ | 3 | 4T4 | 3375000 |

$D_{6}$ | 2 | 6T2 | 22500 |

$D_{7}$ | 2 | 7T2 | 40000 |

$S_{3}C_3$ | 2 | 6T5 | 2828 |

$F_{5}$ | 4 | 7T3 | 1600000000 |

$S_{4}$ | 3 | 4T5 | 22497 |

$S_{4}$ | 3 | 6T8 | 635168 |

$A_{4}C_2$ | 3 | 6T6 | 22497 |

$C_{3}^2:C_4$ | 4 | 6T10 | 3374494 |

$S_{3}^2$ | 3 | 6T9 | 7998219 |

$A_{5}$ | 3 | 12T33 | 66627 |

$A_{5}$ | 4 | 5T4 | 613778 |

$A_{5}$ | 5 | 6T12 | 52222435 |

$S_{5}$ | 4 | 5T5 | 7226 |

$S_{5}$ | 4 | 10T12 | 613778 |

$S_{5}$ | 5 | 6T14 | 52222435 |

$S_{5}$ | 5 | 10T13 | 52222435 |

$S_{5}$ | 6 | 20T35 | 4439177045 |