# SmallGroup(32,9)

From Groupprops

This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this groupView a complete list of particular groups (this is a very huge list!)[SHOW MORE]

## Contents

## Definition

**PLACEHOLDER FOR INFORMATION TO BE FILLED IN**: [SHOW MORE]

## Position in classifications

Get more information about groups of the same order at Groups of order 32#The list

Type of classification | Position/number in classification |
---|---|

GAP ID | , i.e., among groups of order 32 |

Hall-Senior number | 27 among groups of order 32 |

Hall-Senior symbol |

## Arithmetic functions

Want to compare and contrast arithmetic function values with other groups of the same order? Check out groups of order 32#Arithmetic functions

## Group properties

Property | Satisfied? | Explanation | Comment |
---|---|---|---|

group of prime power order | Yes | ||

nilpotent group | Yes | prime power order implies nilpotent | |

supersolvable group | Yes | via nilpotent: finite nilpotent implies supersolvable | |

solvable group | Yes | via nilpotent: nilpotent implies solvable | |

abelian group | No |

## GAP implementation

### Group ID

This finite group has order 32 and has ID 9 among the groups of order 32 in GAP's SmallGroup library. For context, there are 51 groups of order 32. It can thus be defined using GAP's SmallGroup function as:

`SmallGroup(32,9)`

For instance, we can use the following assignment in GAP to create the group and name it :

`gap> G := SmallGroup(32,9);`

Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:

`IdGroup(G) = [32,9]`

or just do:

`IdGroup(G)`

to have GAP output the group ID, that we can then compare to what we want.