# Dihedral group:D14

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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: $G := \langle a,x \mid a^7 = x^2 = e, xax = a^{-1} \rangle$

Here, $e$ 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 $G$:

gap> G := SmallGroup(14,1);

Conversely, to check whether a given group $G$ 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