Abelian [p^2,p] Group

Cyclic group of order p White Sheet

[Class] | [Family] | Samples by Order: [8], [27].

Let p be any prime.

Subgroup Lattice

$C_{p^2} x C_p$

Alternate Descriptions: (* Most common)

Name Symbol(s)

Abelian [p^2,p] * Cp^2 x Cp,
Zp^2 x Zp

GAP ID:?
Magma ID:?

Standard Invariants:

Invariant Value

Abelian True

Nilpotent True

Nilpotency Class 1

Ascending Central Series [0, Cp^2 x Cp]

Descending Central Series [Cp^2 x Cp, 0]

Solvable True

Composition Factors {Cp, Cp, Cp}

Automorphism Group ?

Invariant	Value
Abelian	True
Nilpotent	True
Nilpotency Class	1
Ascending Central Series	[0, Cp^2 x Cp]
Descending Central Series	[Cp^2 x Cp, 0]
Solvable	True
Composition Factors	{Cp, Cp, Cp}
Automorphism Group	?