G:=Group(
(1,2)(3,19)(5,6)(7,20)(8,33)(9,10)(11,12)(13,14)(15,16)(21,53)(22,23)(25,26)
(28,29)(31,32)(34,35)(36,83)(37,38)(40,41)(43,44)(45,46)(47,72)(48,49)(50,51)
(52,62)(54,55)(56,58)(59,93)(60,61)(63,64)(65,100)(66,67)(68,69)(70,71)(73,74)
(75,82)(76,77)(78,79)(80,81)(90,91)(94,99),
(1,6,8,7,5)(2,3,4,32,9)(10,75,76,55,11)(12,85,57,56,13)(14,53,99,44,15)(16,54,
19,18,17)(20,21,22,72,45)(23,52,51,25,24)(26,27,28,83,61)(29,84,68,31,30)
(33,34,74,98,67)(35,60,59,37,36)(38,39,91,92,40)(41,42,58,78,43)(46,73,77,48,
47)(49,50,71,79,70)(62,63,69,80,100)(64,90,89,66,65)(81,82,88,87,86)(93,96,97,
95,94)
); 
F:=FreeGroup(2);
F.relators:=[F.1^2,F.2^5,(F.1*F.2)^10,(F.1*F.2^-2*F.1*F.2^2)^3,
      (F.1*F.2^2*F.1*F.2^-1)^7,
      (F.1*F.2^2)^2*F.1*F.2^-2*(F.1*F.2^-1*F.1*F.2^2*F.1*F.2*F.1*F.2^2)^2];
K:=Subgroup(F,[F.1*F.2^2*F.1*F.2^-2*F.1,(F.2*F.1*F.2)^2]);
