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Dihedral group:D10


This group is defined as the dihedral group of order ten. In other words, it is the semidirect product of the cyclic group of order five and a cyclic group of order two.

Arithmetic functions

Function Value Explanation
order 10
exponent 10
Fitting length 2
Frattini length 1
derived length 2

Group properties

GAP implementation

Group ID

This finite group has order 10 and has ID 1 among the groups of order 10 in GAP's SmallGroup library. For context, there are groups of order 10. It can thus be defined using GAP's SmallGroup function as:


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

gap> G := SmallGroup(10,1);

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

IdGroup(G) = [10,1]

or just do:


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

Other descriptions

This group can be defined using GAP's DihedralGroup function: