Cyclic group of order 8 White Sheet [Printable Version]

Subgroup Lattice	Element Lattice

Alternate Descriptions: (* Most common)

Name	Symbol(s)
* Cyclic	* C8, Z8
Abelian [8]

GAP ID: [8,1]
Magma ID:?

Standard Invariants:

Invariant	Value
Abelian	True
Nilpotent	True
Nilpotency Class	1
Ascending Central Series	[0,C8]
Descending Central Series	[C8,0]
Solvable	True
Composition Factors	{C2, C2, C2}
Automorphism Group	C2 x C2

Permutation Representations [Description]

Action Name	Degree	Generators	Stabilizer (Isomorphism Type)	Stabilizer (Genertors)	Primitivity Blocks
	[Description]		[Description]	[Description]	[Description]
Regular	8	(12345678)	0	()	{1,3,5,7},{2,4,6,8}