Direct product of Z8 and Z4 and Z2
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This group can be defined in the following equivalent ways:
- It is the external direct product of cyclic group:Z8, cyclic group:Z4, and cyclic group:Z2.
- It is the external direct product of direct product of Z8 and Z4 and cyclic group:Z2.
- It is the external direct product of direct product of Z8 and Z2 and cyclic group:Z4.
- It is the external direct product of direct product of Z4 and Z2 and cyclic group:Z8.
As an abelian group of prime power order
This group is the abelian group of prime power order corresponding to the partition:
In other words, it is the group .
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 83 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(64,83);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [64,83]
or just do:
to have GAP output the group ID, that we can then compare to what we want.
|DirectProduct(CyclicGroup(8),CyclicGroup(4),CyclicGroup(2))||DirectProduct and CyclicGroup|