Copyright (c) 2004 James B. Wilson | Show Frames | Hide Frames

Cyclic group of order p White Sheet

Other Group White Sheets
[Class] | [Family] | Samples by Order: [8], [27].

Let p be any prime.

Subgroup Lattice
Alternate Descriptions: (* Most common)
Name Symbol(s)
*Elementary
Abelian
EA(p^3)
Abelian [p,p,p] * Cp x Cp x Cp,
Zp x Zp x Zp

GAP ID:?
Magma ID:?

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