Dihedral Group D8 White Sheet [Printable Version]

Subgroup Lattice	Element Lattice	Conjugated Post-Lattice

Alternate Descriptions: (* Most common)

Name	Symbol(s)
* Quaternion	* Q8
Extraspecial ("-" Type)	E-(8)

GAP ID: [8,4]
Magma ID:?

Standard Invariants:

Invariant	Value
Abelian	False
Nilpotent	True
Nilpotency Class	2
Ascending Central Series	[0, C2, Q8]
Descending Central Series	[Q8, C2, 0]
Solvable	True
Composition Factors	{C2, C2, C2}
Automorphism Group

Permutation Representations [Description]

Action Name	Degree	Generators	Stabilizer (Isomorphism Type)	Stabilizer (Genertors)	Primitivity Blocks
	[Description]		[Description]	[Description]	[Description]
Regular	8	(1256)(3478) (1357)(8642)	0	()	{{1,3,5,7},{2,4,6,8}}