Cyclic Group of Order 16

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Copyright (c) 2003-2004 James B. Wilson

Cyclic group of order 16 White Sheet [Printable Version]

Subgroup Lattice Element Lattice

$C_{16}$ $C_{16}$

Alternate Descriptions: (* Most common)

Name Symbol(s)

* Cyclic * C16, Z16

Abelian [16]

GAP ID: [16,1]
Magma ID:?

Standard Invariants:

Invariant Value

Abelian True

Nilpotent True

Nilpotency Class 1

Ascending Central Series [0,C16]

Descending Central Series [C16,0]

Solvable True

Composition Factors {C2, C2, C2, C2}

Automorphism Group C4 x C2

Permutation Representations [Description]

Action Name
Degree
Generators
Stabilizer
(Isomorphism Type) Stabilizer
(Genertors)
Primitivity Blocks

[Description] [Description] [Description] [Description]

Regular 16 (1,...,16) 0 () {1,3,5,7,...},{2,4,6,8,...}

Invariant	Value
Abelian	True
Nilpotent	True
Nilpotency Class	1
Ascending Central Series	[0,C16]
Descending Central Series	[C16,0]
Solvable	True
Composition Factors	{C2, C2, C2, C2}
Automorphism Group	C4 x C2

Action Name	Degree	Generators	Stabilizer (Isomorphism Type)	Stabilizer (Genertors)	Primitivity Blocks
	[Description]		[Description]	[Description]	[Description]
Regular	16	(1,...,16)	0	()	{1,3,5,7,...},{2,4,6,8,...}