#
#                         +--------------+
#                         |  1    2    3 |
#                         |  4  top    5 |
#                         |  6    7    8 |
#          +--------------+--------------+--------------+--------------+
#          |  9   10   11 | 17   18   19 | 25   26   27 | 33   34   35 |
#          | 12  left  13 | 20 front  21 | 28 right  29 | 36  rear  37 |
#          | 14   15   16 | 22   23   24 | 30   31   32 | 38   39   40 |
#          +--------------+--------------+--------------+--------------+
#                         | 41   42   43 |
#                         | 44 bottom 45 |
#                         | 46   47   48 |
#                         +--------------+
#


gap> top   := ( 1, 3, 8, 6)( 2, 5, 7, 4)( 9,33,25,17)(10,34,26,18)(11,35,27,19);;
gap> 
gap> left  := ( 9,11,16,14)(10,13,15,12)( 1,17,41,40)( 4,20,44,37)( 6,22,46,35);;
gap> 
gap> front := (17,19,24,22)(18,21,23,20)( 6,25,43,16)( 7,28,42,13)( 8,30,41,11);;
gap> 
gap> right := (25,27,32,30)(26,29,31,28)( 3,38,43,19)( 5,36,45,21)( 8,33,48,24);;
gap> 
gap> rear  := (33,35,40,38)(34,37,39,36)( 3, 9,46,32)( 2,12,47,29)( 1,14,48,27);;
gap> 
gap> bottom:= (41,43,48,46)(42,45,47,44)(14,22,30,38)(15,23,31,39)(16,24,32,40);;
gap> G:=Group(top,bottom,front^2,rear^2,right,left);
Group( ( 1, 3, 8, 6)( 2, 5, 7, 4)( 9,33,25,17)(10,34,26,18)(11,35,27,19), 
(14,22,30,38)(15,23,31,39)(16,24,32,40)(41,43,48,46)(42,45,47,44), ( 6,43)
( 7,42)( 8,41)(11,30)(13,28)(16,25)(17,24)(18,23)(19,22)(20,21), ( 1,48)
( 2,47)( 3,46)( 9,32)(12,29)(14,27)(33,40)(34,39)(35,38)(36,37), ( 3,38,43,19)
( 5,36,45,21)( 8,33,48,24)(25,27,32,30)(26,29,31,28), ( 1,17,41,40)
( 4,20,44,37)( 6,22,46,35)( 9,11,16,14)(10,13,15,12) )
gap> G0:=Group(top,bottom,front,rear,right,left);
Group( ( 1, 3, 8, 6)( 2, 5, 7, 4)( 9,33,25,17)(10,34,26,18)(11,35,27,19), 
(14,22,30,38)(15,23,31,39)(16,24,32,40)(41,43,48,46)(42,45,47,44), 
( 6,25,43,16)( 7,28,42,13)( 8,30,41,11)(17,19,24,22)(18,21,23,20), 
( 1,14,48,27)( 2,12,47,29)( 3, 9,46,32)(33,35,40,38)(34,37,39,36), 
( 3,38,43,19)( 5,36,45,21)( 8,33,48,24)(25,27,32,30)(26,29,31,28), 
( 1,17,41,40)( 4,20,44,37)( 6,22,46,35)( 9,11,16,14)(10,13,15,12) )
gap> N0:=Size(G0);
43252003274489856000
gap> N:=Size(G);
21119142223872000
gap> q:=N0/N;
2048
gap> FactorInt(q);
Error, Variable: 'FactorInt' must have a value
gap> 2^(11);
2048
gap> flip:=(21,28)(20,13);
(13,20)(21,28)
gap> flip in G0;
true
gap> flip in G;
false
gap> n:=8*7*6*5*4*3*2*3^7*12*11*10*9*8*7*6*5*4*3*2/2;
21119142223872000
gap> quit;