gap> P:=SylowSubgroup(MathieuGroup(12),2);;
gap> R:=ResolutionPrimePowerGroup(P,20);
Resolution of length 20 in characteristic 2 for Group(
[ (2,8,4,12)(3,11,7,9), (2,3)(4,7)(6,10)(9,11), (3,7)(6,10)(8,11)(9,12), 
  (1,10)(3,7)(5,6)(8,12), (2,4)(3,7)(8,12)(9,11), (1,5)(6,10)(8,12)(9,11) 
 ]) . 

gap> Size(R);
[ 6, 62, 282, 740, 1810, 3518, 6440, 10600, 17040, 24162, 34774, 49874, 
  62416, 81780, 106406, 145368, 172282, 208926, 262938, 320558 ]
