# 16Gamma2c

From Groupprops

Template:Particular Hall-Senior genus

## Contents

## Definition

### The lattice of normal subgroups with families indicated

It is member of the Hall-Senior family for groups of order .

### Members

There are two members:

Member name | Hall-Senior symbol | Second part of GAP ID | Hall-Senior number |
---|---|---|---|

SmallGroup(16,3) | 3 | 9 | |

SmallGroup(16,4) | 4 | 10 |

## Arithmetic functions

### Arithmetic functions with unambiguous values by definition of genus

These are arithmetic functions whose values are unambiguous by the definition of Hall-Senior genus for groups of a given order.

Function | Value | Explanation |
---|---|---|

order | 16 | |

prime-base logarithm of order | 4 | |

nilpotency class | 2 | |

derived length | 2 | |

Frattini length | 2 | |

prime-base logarithm of order of inner automorphism group | 2 | |

prime-base logarithm of order of derived subgroup | 3 |

### Arithmetic function values for both members

Note that some of these arithmetic function values are the same for both members, but this is true only because of the particular genus.