# Direct product of A4 and Z5

From Groupprops

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## Contents

## Definition

This group is defined as the external direct product of alternating group:A4 and cyclic group:Z5.

## Arithmetic functions

Want to compare and contrast arithmetic function values with other groups of the same order? Check out groups of order 60#Arithmetic functions

## GAP implementation

### Group ID

This finite group has order 60 and has ID 9 among the groups of order 60 in GAP's SmallGroup library. For context, there are 13 groups of order 60. It can thus be defined using GAP's SmallGroup function as:

`SmallGroup(60,9)`

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

`gap> G := SmallGroup(60,9);`

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

`IdGroup(G) = [60,9]`

or just do:

`IdGroup(G)`

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

### Other descriptions

Description | Functions used |
---|---|

DirectProduct(AlternatingGroup(4),CyclicGroup(5)) |
AlternatingGroup, CyclicGroup |