# Dihedral group:D14

From Groupprops

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## Definition

The group is defined as the dihedral group of degree 7 and hence order 14. It is given explicitly by the presentation:

Here, denotes the identity element.

## GAP implementation

### Group ID

This finite group has order 14 and has ID 1 among the groups of order 14 in GAP's SmallGroup library. For context, there are groups of order 14. It can thus be defined using GAP's SmallGroup function as:

`SmallGroup(14,1)`

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

`gap> G := SmallGroup(14,1);`

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

`IdGroup(G) = [14,1]`

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 |
---|---|

DihedralGroup(14) |
DihedralGroup |