# Classification of groups of order 2^n

This article gives information on the classification process for groups of order 2^n. All groups of order have been classified for . The classification problem becomes more messy and huge as gets larger.

Number of groups of order | Information on groups of order | Information on classification | ||
---|---|---|---|---|

0 | 1 | 1 | trivial group only | -- |

1 | 2 | 1 | cyclic group:Z2 only | equivalence of definitions of group of prime order |

2 | 4 | 2 | groups of order 4 | classification of groups of prime-square order |

3 | 8 | 5 | groups of order 8 | classification of groups of prime-cube order, the case of differs somewhat from the case of , odd |

4 | 16 | 14 | groups of order 16 | classification of groups of order 16 |

5 | 32 | 51 | groups of order 32 | classification of groups of order 32 |

6 | 64 | 267 | groups of order 64 | classification of groups of order 64 |

7 | 128 | 2328 | groups of order 128 | classification of groups of order 128 |

8 | 256 | 56092 | groups of order 256 | classification of groups of order 256 |

9 | 512 | 10494213 | groups of order 512 | classification of groups of order 512 |

10 | 1024 | 49487365422 | groups of order 1024 | classification of groups of order 1024 |