gap> FRU:= (6, 16, 21)(7, 18, 25)(10, 17, 24)(8, 19, 22)(2,30,12);;
gap> BRU:= (21, 16, 26)(22, 17, 30)(25, 20, 29)(23, 18, 27)(5,13,7);;
gap> BLU:= (26 ,16, 1)(27, 20, 5)(28, 17, 2)(30, 19, 4)(14,22,10);;
gap> FLU:= (1, 16, 6)(2, 19, 10)(5, 18, 9)(3, 20, 7)(27,25,15);;
gap> DFR:= (11, 6, 21)(25, 13, 9)(23, 15, 7)(24, 12, 8)(3,18,29);;
gap> BDR:= (26, 11, 21)(29, 13, 23)(27, 12, 22)(30, 14, 24)(8,17,4);;
gap> DFL:= (6, 11, 1)(9, 15, 3)(10, 12, 4)(8, 14, 2)(24,28,19);;
gap> BDL:= (1, 11, 26)(3, 13, 27)(4, 14, 28)(5, 15, 29)(23,20,9);;
gap> G1:=Group(FRU,FLU,BRU,BLU,BDR,BDL,DFR,DFL);
Group( ( 2,30,12)( 6,16,21)( 7,18,25)( 8,19,22)(10,17,24), ( 1,16, 6)
( 2,19,10)( 3,20, 7)( 5,18, 9)(15,27,25), ( 5,13, 7)(16,26,21)(17,30,22)
(18,27,23)(20,29,25), ( 1,26,16)( 2,28,17)( 4,30,19)( 5,27,20)(10,14,22), 
( 4, 8,17)(11,21,26)(12,22,27)(13,23,29)(14,24,30), ( 1,11,26)( 3,13,27)
( 4,14,28)( 5,15,29)( 9,23,20), ( 3,18,29)( 6,21,11)( 7,23,15)( 8,24,12)
( 9,25,13), ( 1, 6,11)( 2, 8,14)( 3, 9,15)( 4,10,12)(19,24,28) )
gap> N1:=Size(G1);
111680712311983099084800000
gap> RUF := ( 1,11,17) ( 2,12,20)( 4,10,18)(22, 6,14) (25,27,29);
( 1,11,17)( 2,12,20)( 4,10,18)( 6,14,22)(25,27,29)
gap>      RUB := ( 2,10,22) ( 1, 9,23)( 3,11,21)(17, 5,15) (25,27,30);
( 1, 9,23)( 2,10,22)( 3,11,21)( 5,15,17)(25,27,30)
gap>      LUF := ( 6,12,18) ( 5,11,19)( 7, 9,17)(21, 1,13) (26,27,29);
( 1,13,21)( 5,11,19)( 6,12,18)( 7, 9,17)(26,27,29)
gap>      LUB := ( 5, 9,21) ( 6,10,24)( 8,12,22)(18, 2,16) (26,27,30);
( 2,16,18)( 5, 9,21)( 6,10,24)( 8,12,22)(26,27,30)
gap>      RDF := ( 4,14,20) ( 1,15,19)( 3,13,17)( 7,11,23) (25,28,29);
( 1,15,19)( 3,13,17)( 4,14,20)( 7,11,23)(25,28,29)
gap>      RDB := ( 3,15,23) ( 2,14,24)( 4,16,22)( 8,10,20) (25,28,30);
( 2,14,24)( 3,15,23)( 4,16,22)( 8,10,20)(25,28,30)
gap>      LDF := ( 7,13,19) ( 6,16,20)( 8,14,18)( 4,12,24) (26,28,29);
( 4,12,24)( 6,16,20)( 7,13,19)( 8,14,18)(26,28,29)
gap>      LDB := ( 8,16,24) ( 5,13,23)( 7,15,21)( 3, 9,19) (26,28,30);
( 3, 9,19)( 5,13,23)( 7,15,21)( 8,16,24)(26,28,30)
gap> G:=Group(LUB, LUF, RUB, RUF, LDB, LDF, RDB, RDF);
Group( ( 2,16,18)( 5, 9,21)( 6,10,24)( 8,12,22)(26,27,30), ( 1,13,21)
( 5,11,19)( 6,12,18)( 7, 9,17)(26,27,29), ( 1, 9,23)( 2,10,22)( 3,11,21)
( 5,15,17)(25,27,30), ( 1,11,17)( 2,12,20)( 4,10,18)( 6,14,22)(25,27,29), 
( 3, 9,19)( 5,13,23)( 7,15,21)( 8,16,24)(26,28,30), ( 4,12,24)( 6,16,20)
( 7,13,19)( 8,14,18)(26,28,29), ( 2,14,24)( 3,15,23)( 4,16,22)( 8,10,20)
(25,28,30), ( 1,15,19)( 3,13,17)( 4,14,20)( 7,11,23)(25,28,29) )
gap> N:=Size(G);
37791360
gap> N/12;
3149280
gap> 100776960/2^5;
3149280
gap> 4*3*2*6*5*4*3*2*3^7/4;
9447840
gap> M:=4*3*2*6*5*4*3*2*3^7/4;
9447840
gap> M*3;
28343520
gap> M/3;
3149280
gap> M*4;
37791360
gap> quit;