Cyclic group of order 3 White Sheet [Printable Version]

Group Class

Subgroup Lattice	Element Lattice

Alternate Descriptions: (* Most common)

Name	Symbol(s)
* Cyclic	* C3, Z3
Abelian [3]

GAP ID: [3,1]
Magma ID:?

Standard Invariants:

Invariant	Value
Abelian	True
Nilpotent	True
Nilpotency Class	1
Ascending Central Series	[0,C3]
Descending Central Series	[C3,0]
Solvable	True
Composition Factors	{C3}
Automorphism Group	C2

Permutation Representations [Description]

Action Name	Degree	Generators	Stabilizer (Isomorphism Type)	Stabilizer (Genertors)	Primitivity Blocks
	[Description]		[Description]	[Description]	[Description]
Regular	3	(123)	0	()	Primitive