An answer to K. Ewald's queastion to the gap forum:

There is a function UpperCentralSeriesOfGroup which is called with the
group in question as argument.

Alternatively, if you want to do the calculation more explicitly, you
could do the following: given Zi, make the factor group G/Zi with
NaturalHomomorphismByNormalSubgroup, compute its centre, and take the
inverse image of that centre under the homomorphism (perhaps using
InverseGeneralMapping). This way, it is clear that the definition
> Zi+1(G) / Zi(G) = Centre(G / Zi(G).
can be made constructive.

I hope this helps,

Jan Draisma.