## Distribution of groups in curves of genus 2

Isomorphism class | GAP/Magma Group | Distinct generating vectors |
---|---|---|

$C_2$ | [2,1] | 1 |

$C_3$ | [3,1] | 1 |

$C_4$ | [4,1] | 1 |

$C_2^2$ | [4,2] | 3 |

$C_5$ | [5,1] | 4 |

$S_3$ | [6,1] | 2 |

$C_6$ | [6,2] | 3 |

$C_8$ | [8,1] | 2 |

$D_4$ | [8,3] | 1 |

$Q_8$ | [8,4] | 1 |

$C_{10}$ | [10,2] | 4 |

$C_3:C_4$ | [12,1] | 1 |

$D_6$ | [12,4] | 1 |

$C_2\times C_6$ | [12,5] | 6 |

$SD_{16}$ | [16,8] | 2 |

$\SL(2,3)$ | [24,3] | 1 |

$C_3:D_4$ | [24,8] | 2 |

$\GL(2,3)$ | [48,29] | 2 |