Dennis Drapeau asks:

I would like to know how to save(to disk) the groups that GAP creates so that I
do not have to wait for GAP to redo any lengthy computations everytime I start u
p the program.

The simplest thing you can do is use the PrintTo() and AppendTo() functions to
print the group to a file. For example:

gap> g := Group((1,2)(3,4),(1,3)(2,4));
Group( (1,2)(3,4), (1,3)(2,4) )
gap> PrintTo("filename","g := ",g,";\n");
gap> Unbind(g);
gap> g;
Error, Variable: 'g' must have a value
gap> Read("filename");
gap> g;
Group( (1,2)(3,4), (1,3)(2,4) )
gap>  quit;
11.820u 2.690s 1:24.83 17.1% 0+3865k 85+4io 83pf+0w
{keith:584} cat filename
g := Group( (1,2)(3,4), (1,3)(2,4) );
{keith:585}

This will work for permutation groups or matrix groups, for example, but not so
well for finitely-presented groups. You also lose some of the extra information
that GAP can store in the group record, which can take time to recover.

Steve