Elementary Abelain Group of Order 8

C2 x C2 x C2 White Sheet [Printable Version]

Subgroup Lattice

Element Lattice

3-D Lattice

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Alternate Descriptions: (* Most common)

Name Symbol(s)

* Elementary Abelian EA(8)

Abelian [2,2,2] * C2 x C2 x C2

GAP ID: [8,5]
Magma ID:?

Standard Invariants:

Invariant Value

Abelian True

Nilpotent True

Nilpotency Class 1

Ascending Central Series [0, C2 x C2 x C2]

Descending Central Series [C2 x C2 x C2, 0]

Solvable True

Composition Factors {C2, C2, C2}

Automorphism Group GL3(2)

Permutation Representations [Description]

Action Name
Degree
Generators
Stabilizer
(Isomorphism Type) Stabilizer
(Genertors)
Primitivity Blocks

[Description] [Description] [Description] [Description]

Regular 8 (1234)(5678), (15)(26)(37)(48) 0 () {1,2,3,4},{5,6,7,8}

Name	Symbol(s)
* Elementary Abelian	EA(8)
Abelian [2,2,2]	* C2 x C2 x C2

Invariant	Value
Abelian	True
Nilpotent	True
Nilpotency Class	1
Ascending Central Series	[0, C2 x C2 x C2]
Descending Central Series	[C2 x C2 x C2, 0]
Solvable	True
Composition Factors	{C2, C2, C2}
Automorphism Group	GL3(2)

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