# Cyclic group:Z36

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## Definition

This group can be defined in the following equivalent ways:

- It is the cyclic group, and specifically finite cyclic group, of order 36.
- It is the external direct product of cyclic group:Z4 and cyclic group:Z9.

## GAP implementation

### Group ID

This finite group has order 36 and has ID 2 among the groups of order 36 in GAP's SmallGroup library. For context, there are groups of order 36. It can thus be defined using GAP's SmallGroup function as:

`SmallGroup(36,2)`

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

`gap> G := SmallGroup(36,2);`

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

`IdGroup(G) = [36,2]`

or just do:

`IdGroup(G)`

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

### Other descriptions

Descriptions | Functions used |
---|---|

CyclicGroup(36) |
CyclicGroup |

DirectProduct(CyclicGroup(4),CyclicGroup(9)) |
DirectProduct, CyclicGroup |