B. Leisure and Recreation: Cohomology Rings of all Groups of Size 16
  
  Below  is the output of the test file tst/batch.g. The file runs through all
  groups  of size n, which is initially set to 16, calls ProjectiveResolution,
  CohomologyGenerators,  and CohomologyRelators for each group, and prints the
  results,  as well as the runtimes for each operation, to a file like the one
  shown  below.  The  runtimes  in this example have been deleted, having been
  presented  in Appendix A.. The example below was computed on a 2.4 GHz AMD64
  processor  with  12  GB  of  RAM. See the file tst/README for suggestions on
  dealing with other users when running long-running batch processes.
  
  -----------------------------  Log  ------------------------------
    
    SmallGroup(16,1)
    Betti Numbers: [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
    Generators in degrees: [ 1, 2 ]
    Relators: [ [ z, y ], [ z^2 ] ]
    
    SmallGroup(16,2)
    Betti Numbers: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ]
    Generators in degrees: [ 1, 1, 2, 2 ]
    Relators: [ [ z, y, x, w ], [ z^2, y^2 ] ]
    
    SmallGroup(16,3)
    Betti Numbers: [ 1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36 ]
    Generators in degrees: [ 1, 1, 2, 2, 2 ]
    Relators: [ [ z, y, x, w, v ], [ z^2, z*y, z*x, y^2*v+x^2 ] ]
    
    SmallGroup(16,4)
    Betti Numbers: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ]
    Generators in degrees: [ 1, 1, 2, 2 ]
    Relators: [ [ z, y, x, w ], [ z^2, z*y+y^2, y^3 ] ]
    
    SmallGroup(16,5)
    Betti Numbers: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ]
    Generators in degrees: [ 1, 1, 2 ]
    Relators: [ [ z, y, x ], [ z^2 ] ]
    
    SmallGroup(16,6)
    Betti Numbers: [ 1, 2, 2, 2, 3, 4, 4, 4, 5, 6, 6 ]
    Generators in degrees: [ 1, 1, 3, 4 ]
    Relators: [ [ z, y, x, w ], [ z^2, z*y^2, z*x, x^2 ] ]
    
    SmallGroup(16,7)
    Betti Numbers: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ]
    Generators in degrees: [ 1, 1, 2 ]
    Relators: [ [ z, y, x ], [ z*y ] ]
    
    SmallGroup(16,8)
    Betti Numbers: [ 1, 2, 2, 2, 3, 4, 4, 4, 5, 6, 6 ]
    Generators in degrees: [ 1, 1, 3, 4 ]
    Relators: [ [ z, y, x, w ], [ z*y, z^3, z*x, y^2*w+x^2 ] ]
    
    SmallGroup(16,9)
    Betti Numbers: [ 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2 ]
    Generators in degrees: [ 1, 1, 4 ]
    Relators: [ [ z, y, x ], [ z*y, z^3+y^3, y^4 ] ]
    
    SmallGroup(16,10)
    Betti Numbers: [ 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66 ]
    Generators in degrees: [ 1, 1, 1, 2 ]
    Relators: [ [ z, y, x, w ], [ z^2 ] ]
    
    SmallGroup(16,11)
    Betti Numbers: [ 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66 ]
    Generators in degrees: [ 1, 1, 1, 2 ]
    Relators: [ [ z, y, x, w ], [ z*y ] ]
    
    SmallGroup(16,12)
    Betti Numbers: [ 1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17 ]
    Generators in degrees: [ 1, 1, 1, 4 ]
    Relators: [ [ z, y, x, w ], [ z^2+z*y+y^2, y^3 ] ]
    
    SmallGroup(16,13)
    Betti Numbers: [ 1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17 ]
    Generators in degrees: [ 1, 1, 1, 4 ]
    Relators: [ [ z, y, x, w ], [ z*y+x^2, z*x^2+y*x^2, y^2*x^2+x^4 ] ]
    
    SmallGroup(16,14)
    Betti Numbers: [ 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286 ]
    Generators in degrees: [ 1, 1, 1, 1 ]
    Relators: [ [ z, y, x, w ], [  ] ]
    
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