Why can't I compute the irreducible representation and character table of `AffineCrystGroup`?

Question

See the following example code snippets in GAP:

gap> M1:=[[0,0,1,0],[1,0,0,0],[0,-1,0,0],[1/4,1/4,1/4,1]];;
gap> M2:=[[0,0,-1,0],[0,-1,0,0],[1,0,0,0],[0,0,0,1]];;
gap> S:=AffineCrystGroup([M1,M2]);
<matrix group with 2 generators>
gap> Size(S);
infinity
gap> IrreducibleRepresentations(S);
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 2nd choice method found for `IrreducibleRepresentations' on 1 arguments at /home/werner/Public/repo/github.com/gap-system/gap.git/lib/methsel2.g:249 called from
<function "HANDLE_METHOD_NOT_FOUND">( <arguments> )
 called from read-eval loop at *stdin*:5
type 'quit;' to quit to outer loop
brk> Irr(S);
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 4th choice method found for `ConjugacyClasses' on 1 arguments at /home/werner/Public/repo/github.com/gap-system/gap.git/lib/methsel2.g:249 called from
ConjugacyClasses( G ) at /home/werner/Public/repo/github.com/gap-system/gap.git/lib/ctbl.gi:1077 called from
OrdinaryCharacterTable( G ) at /home/werner/Public/repo/github.com/gap-system/gap.git/lib/ctbl.gi:810 called from
Irr( G, 0 ) at /home/werner/Public/repo/github.com/gap-system/gap.git/lib/ctbl.gi:792 called from
ErrorNoReturn( no_method_found ); at /home/werner/Public/repo/github.com/gap-system/gap.git/lib/methsel2.g:249 called from
<function "HANDLE_METHOD_NOT_FOUND">( <arguments> )
 called from read-eval loop at *errin*:1
type 'quit;' to quit to outer loop

It's well known that Space Groups Irreducible Representations and character table exist. Why can't these things be directly calculated in GAP?

Regards, HZ

Answer 1

I am going to answer the question from the title. Space groups are infinite. They in general admit infinitely many irreducible representations, and can't in general be computed algorithmically.

Also, character tables are for finite groups.