Dihedral Group D8 White Sheet [Printable Version]

Subgroup Lattice	Element Lattice
Conjugated Post-Lattice

Alternate Descriptions: (* Most common)

Name	Symbol(s)
* Dihedral	* D8 D4
Extraspecial ("+" Type)	E+(8)

GAP ID: [8,3]
Magma ID:?

Standard Invariants:

Invariant	Value
Abelian	False
Nilpotent	True
Nilpotency Class	2
Ascending Central Series	[0, C2, D8]
Descending Central Series	[D8, C2, 0]
Solvable	True
Composition Factors	{C2, C2, C2}
Automorphism Group	D8

Permutation Representations [Description]

Action Name	Degree	Generators	Stabilizer (Isomorphism Type)	Stabilizer (Genertors)	Primitivity Blocks
	[Description]		[Description]	[Description]	[Description]
Dihedral	4	(1234), (13)	C2	(13)	{{1,3},{2,4}}
Regular	8	(1234)(5678), (15)(26)(37)(48)	0	()	{{1,3,5,7},{2,4,6,8}}