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, denoted , , or , is defined in the following equivalent ways:
- It is the unique (up to isomorphism) cyclic group of order 40, i.e., it is a group of integers modulo n where .
- It is the external direct product of cyclic group:Z8 and cyclic group:Z5, i.e., is it .
This finite group has order 40 and has ID 2 among the groups of order 40 in GAP's SmallGroup library. For context, there are groups of order 40. 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(40,2);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [40,2]
or just do:
to have GAP output the group ID, that we can then compare to what we want.