This chapter describes functions which may be used to perform certain cohomological calculations on a finite group G.
These include:
All of these functions require G to be defined as a finite permutation
group. The functions which compute presentations require, in addition, a
presentation of G. Finally, the functions which operate on a module M
require the module to be defined by a list of matrices over K. This
situation is handled by first defining a {GAP} record, which contains the
required information. This is done using the function CHR, which must be
called before any of the other functions. The remaining functions operate
on this record.
If no presentation of the permutation group G is known, and G has
order at most 32767, then a presentation can be computed using the
function CalcPres. On the other hand, if you start with a finitely
presented group, then you can create a permutation representation
with the function PermRep (although there is no guarantee that the
representation will be faithful ingeneral).
The functions all compute and make use of a descending sequence of subgroups of G, starting at G and ending with a Sylow p-subgroup of G, and it is usually most efficient to have the indices of the subgroups in this chain as small as possible. If you get a warning message, and one of the function fails because the indices in the chain computed are too large, then you can try to remedy matters by supplying your own chain. See Section Further Information for more details, and an example.
If you set the external variable InfoCohomolofy to the value Print,
then a small amount of information will be printed, indicating what is
happening. If chr is the cohomology record you are working with, and
you set the field chr.verbose to the value true, then you will
see all the output of the external programs.
GAP 3.4.4