Direct product of Z10 and Z2
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 direct product of the cyclic group of order ten and the cyclic group of order two.
- It is the direct product of the cyclic group of order five and the Klein four-group.
- It is the direct product of the cyclic group of order five and two copies of the cyclic group of order two.
|order (number of elements, equivalently, cardinality or size of underlying set)||20||groups with same order|
|exponent of a group||10||groups with same order and exponent of a group | groups with same exponent of a group|
|Frattini length||1||groups with same order and Frattini length | groups with same Frattini length|
|Fitting length||1||groups with same order and Fitting length | groups with same Fitting length|
|derived length||1||groups with same order and derived length | groups with same derived length|
|minimum size of generating set||2||groups with same order and minimum size of generating set | groups with same minimum size of generating set|
This finite group has order 20 and has ID 5 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(20,5);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [20,5]
or just do:
to have GAP output the group ID, that we can then compare to what we want.