Direct product of Z4 and Z4

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Definition

This group is defined in the following equivalent ways:

• It is a homocyclic group of order sixteen and exponent four.
• It is the direct product of two copies of cyclic group:Z4.

Arithmetic functions

Function	Value	Explanation
order	16
exponent	4
nilpotency class	1
derived length	1
Frattini length	2
Fitting length	1
minimum size of generating set	2
subgroup rank	2
rank	2
normal rank	2
characteristic rank	2

Group properties

Property	Satisfied	Explanation	Comment
Abelian group	Yes	Direct product of cyclic groups
Nilpotent group	Yes	Abelian implies nilpotent
Metacyclic group	Yes
Supersolvable group	Yes
Solvable group	Yes

GAP implementation

Group ID

The group has ID $2$ among the groups of order sixteen, so it can be defined using GAP's GAP:SmallGroup function:

SmallGroup(16,2)

Other descriptions

The group can also be defined using GAP's DirectProduct function:

DirectProduct(CyclicGroup(4),CyclicGroup(4))