This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this group
View a complete list of particular groups (this is a very huge list!)[SHOW MORE]
This group is defined in the following equivalent ways:
- It is the dihedral group of order .
- It is the direct product of the dihedral group of order ten and the cyclic group of order two.
This finite group has order 20 and has ID 4 among the groups of order 20 in GAP's SmallGroup library. For context, there are 5 groups of order 20. 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 :
gap> G := SmallGroup(20,4);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [20,4]
or just do:
to have GAP output the group ID, that we can then compare to what we want.