gap> dodsl := Group (
>  (1,9,7,5,3)(50,40,30,200,11)(52,42,32,22,13)(2,10,8,6,4)(51,41,31,21,12)
>  (108,106,104,102,100)(88,78,66,110,98)(86,76,64,118,96)(109,107,105,103,101)(87,77,65,119,97),
>  (11,13,15,17,19)(3,200,72,62,54)(5,28,70,60,52)(12,14,16,18,20)(4,29,71,61,53)
>  (98,96,94,92,90)(86,102,112,48,36)(84,100,110,46,34)(99,97,95,93,91)(85,101,111,47,35),
>  (200,22,24,26,28)(5,30,82,74,15)(7,38,80,72,13)(21,23,25,27,29)(6,39,81,73,14)
>  (118,116,114,112,110)(104,68,58,46,96)(102,66,56,44,94)(119,117,115,113,111)(103,67,57,45,95),
>  (30,32,34,36,38)(7,40,92,84,24)(9,48,90,82,22)(31,33,35,37,39)(8,49,91,83,23)
>  (68,66,64,62,60)(56,118,106,70,19)(54,116,104,78,17)(69,67,65,63,61)(55,117,105,79,18),
>  (40,42,44,46,48)(9,50,114,94,34)(1,58,112,92,32)(41,43,45,47,49)(10,59,113,93,33)
>  (78,76,74,72,70)(64,108,80,28,17)(62,106,88,26,15)(79,77,75,73,71)(63,107,89,27,16),
>  (50,52,54,56,58)(1,11,60,116,44)(3,19,68,114,42)(51,53,55,57,59)(2,20,69,115,43)
>  (88,86,84,82,80)(76,100,90,38,26)(74,108,98,36,24)(89,87,85,83,81)(75,109,99,37,25)
>          );;
gap> N:=Size(dodsl);
9627755206121277812101663948800000
gap> n:=Factorial(15)*2^13;
10712468422656000
gap> N/n;
898742925184204800
gap> Factors(N/n);
[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
  2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 7 ]
gap> Factors(Factorial(10));
[ 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 5, 7 ]
gap> Factors(N/(n*Factorial(10)));
[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 
  3, 3, 3, 3, 3, 3, 3 ]
gap> Factors(2^22*3^10);
[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 
  3, 3, 3, 3, 3, 3, 3 ]
gap> quit;