Cyclic group:Z16

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Definition

The cyclic group of order sixteen is the cyclic group having $16$ elements. In other words, it is the quotient of the group of integers $\mathbb{Z}$ by the subgroup $16\mathbb{Z}$ of multiples of $16$.

It is given by the presentation:

$⟨x\mid x^{16}=e⟩$

where $e$ is the identity element.

Arithmetic functions

Function	Value	Explanation
underlying prime of p-group	2
order	16
prime-base logarithm of order	4
exponent	16
prime-base logarithm of exponent	4
nilpotency class	1
derived length	1
Frattini length	4
minimum size of generating set	1
subgroup rank	1
rank as p-group	1
normal rank	1
characteristic rank	1
Fitting length	1

Group properties

Property	Satisfied?	Explanation
cyclic group	Yes
homocyclic group	Yes
metacyclic group	Yes
abelian group	Yes