Dear Forum, dear Nicola Sottocornola,

[...] A and S are 4x4 matrices over Cyclotomics
G:=Group(A,S);;
D:=DerivedSubgroup(G);
K:=Group(GeneratorsOfGroup(D),S);
Size(K);
exceeded the permitted memory (`-o' command line option) at
[...]
brk>

The problem here is the wrong use of the function `Group'. Type

gap> ?Group

to read the manual section for this function.

When it is called as for your group K the second argument is interpreted as
the identity of the group (the first argument is a list of generators).
Since S is not the identity matrix, GAP created a nonsense object here and
runs into an error when you ask for `Size(K);'. We will think about putting
a check of the input into the code in future GAP releases.

What you actually wanted to tell GAP was:

G:=Group(A,S);;
D:=DerivedSubgroup(G);
# Now you just give one list of generators
K:=Group(Concatenation(GeneratorsOfGroup(D), [S]));
Size(K);

I hope this helps,

Frank

///  Dr. Frank Lübeck, Lehrstuhl D für Mathematik, Templergraben 64,  ///
\\\                    52062 Aachen, Germany                          \\\
///  E-mail: Frank.Luebeck@Math.RWTH-Aachen.De                        ///
\\\  WWW:    http://www.math.rwth-aachen.de/~Frank.Luebeck/           \\\