Dihedral group:D18
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Definition
The group is defined as the dihedral group of order math>18</math> and degree . In other words, it has the presentation:
.
GAP implementation
Group ID
This finite group has order 18 and has ID 1 among the groups of order 18 in GAP's SmallGroup library. For context, there are groups of order 18. It can thus be defined using GAP's SmallGroup function as:
SmallGroup(18,1)
For instance, we can use the following assignment in GAP to create the group and name it :
gap> G := SmallGroup(18,1);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [18,1]
or just do:
IdGroup(G)
to have GAP output the group ID, that we can then compare to what we want.
Other descriptions
The group can be constructed using GAP's DihedralGroup function:
DihedralGroup(18)