Direct product of Z4 and Z4 and Z4
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This group is defined in the following equivalent ways:
- It is the external direct product of three copies of cyclic group:Z4.
- It is a homocyclic group of order and exponent .
- It is the cube of the group cyclic group:Z4.
As an abelian group of prime power order
This group is the abelian group of prime power order corresponding to the partition:
and the prime . In other words, it is the group .
|Value of prime number||Corresponding group|
|3||direct product of Z9 and Z9 and Z9|
|5||direct product of Z25 and Z25 and Z25|
Want to compare and contrast arithmetic function values with other groups of the same order? Check out groups of order 64#Arithmetic functions
This finite group has order 64 and has ID 55 among the groups of order 64 in GAP's SmallGroup library. For context, there are groups of order 64. 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(64,55);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [64,55]
or just do:
to have GAP output the group ID, that we can then compare to what we want.