Groups of order p^3

Let p be any prime number. Then there are precisely 5 groups of order p. However, the classification splits into two cases, first if p=2 and the second for all odd primes.

English Name	Symbolic Name	Example p=2	Example p=3
Cyclic	Cp^3	C8	C27
Abelian [p^2,p]	Cp^2 x Cp	C4 x C2	C9 x C3
Abelian [p,p,p]	Cp x Cp x Cp	C2 x C2 x C2	C3 x C3 x C3
[Modular]	Cp^2 * Cp		C9 * C3
Extraspecial	(Cp x Cp) * Cp		(C3 x C3) * C3
Dihedral		D8
Quaternion		Q8