# GAP:DihedralGroup

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## Definition

### Function type

The function takes as input a positive integer (supposed to be even) and outputs a group. An optional filter can be provided.

### Behavior

The function is invoked by:

DihedralGroup([<filt>, ]n)

where $n$ is a positive integer. Here are the possibilities:

Nature of input Output
No filter, $n$ an even integer constructs the dihedral group of order $n$, degree $n/2$ as a PcGroup (i.e., the group is stored in terms of a polycyclic series). The output confirms this
Filter chosen as IsPermGroup, $n$ an even integer the dihedral group of order $n$ is constructed as a permutation group on $n$ letters (note: this is not the same as the default permutation action on $n/2$ letters) $n$ something other than an even integer NoMethodFound error

## Examples of usage

```gap> G := DihedralGroup(8);
<pc group of size 8 with 3 generators>
gap> IdGroup(G);
[ 8, 3 ]
gap> H := DihedralGroup(16);
<pc group of size 16 with 4 generators>
gap> IsSubgroup(H,G);
false
gap> IsPcGroup(H);
true
gap> K := DihedralGroup(IsPermGroup,10);
Group([ (1,2,3,4,5), (2,5)(3,4) ])
gap> Order(K);
10
gap> L := DihedralGroup(31);
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 2nd choice method found for `DihedralGroupCons' on 2 arguments called from
DihedralGroupCons( IsPcGroup, arg ) called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue```