# Direct product of SmallGroup(16,4) and Z2

From Groupprops

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## Contents

## Definition

This group is defined as the external direct product of SmallGroup(16,4) and the cyclic group of order two.

## Position in classifications

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

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

Hall-Senior number | 12 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

## GAP implementation

### Group ID

This finite group has order 32 and has ID 23 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(32,23)`

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

`gap> G := SmallGroup(32,23);`

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

`IdGroup(G) = [32,23]`

or just do:

`IdGroup(G)`

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