# Groups of order 6048

From Groupprops

This article gives information about, and links to more details on, groups of order 6048

See pages on algebraic structures of order 6048| See pages on groups of a particular order

## Statistics at a glance

### Factorization and useful forms

The number 6048 has the following factorization with prime factors 2,3,7:

### Group counts

All groups of this order have not yet been classified. The information below is therefore partial.

Quantity | Value | Explanation |
---|---|---|

Total number of groups up to isomorphism | unknown | |

Number of abelian groups (i.e., finite abelian groups) up to isomorphism | 21 | (Number of abelian groups of order ) times (Number of abelian groups of order ) times (Number of abelian groups of order )= (number of unordered integer partitions of 5) times (number of unordered integer partitions of 3) times (number of unordered integer partitions of 1) = . See classification of finite abelian groups and structure theorem for finitely generated abelian groups. |

Number of nilpotent groups (i.e., finite nilpotent groups) up to isomorphism | 255 | (Number of groups of order 32) times (Number of groups of order 27) times (Number of groups of order 7)= . See number of nilpotent groups equals product of number of groups of order each maximal prime power divisor, which in turn follows from equivalence of definitions of finite nilpotent group. |

Number of solvable groups (i.e., finite solvable groups) up to isomorphism | unknown | |

Number of simple groups up to isomorphism (since the number is composite, this equals the number of simple non-abelian groups) | 1 | projective special unitary group:PSU(3,3) |

Number of almost simple groups up to isomorphism | 1 | same as the simple group |

Number of quasisimple groups up to isomorphism | 1 | same as the simple group |

Number of almost quasisimple groups up to isomorphism | 1 | same as the simple group |

Number of semisimple groups up to isomorphism | 1 | same as the simple group |

Number of perfect groups up to isomorphism | 1 | same as the simple group |