Cyclic group of order p White Sheet [Printable Version]

Let p be any prime number. For example 2 or 3.

Subgroup Lattice	Element Lattice

Alternate Descriptions: (* Most common)

Name	Symbol(s)
* Cyclic	* Cp, Zp
Abelian [p]

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

Standard Invariants:

Invariant	Value
Abelian	True
Nilpotent	True
Nilpotency Class	1
Ascending Central Series	[0,Cp]
Descending Central Series	[Cp,0]
Solvable	True
Composition Factors	{Cp}
Automorphism Group	Cp-1

Permutation Representations [Description]

Action Name	Degree	Generators	Stabilizer (Isomorphism Type)	Stabilizer (Genertors)	Primitivity Blocks
	[Description]		[Description]	[Description]	[Description]
Regular	p	(1,2,.., p)	0	()	Primitive