#gap_J-rubik.txt
#         5  6  7
#         4  H  8
#         3  2  1
#25 28 23|21 26 19|17 32 31|29 30 27
#38 G  36|12 A  10|34 D  40|16 P  14
#43 44 37|39 42 33|35 48 45|47 46 41
#         11 18 9
#         20 B  24
#         13 22 15

# Iso=le groupe isometrie du cube (48)
j1 := (6,46,18,26)(8,14,24,12)(38,48,36,32)(2,30,22,42)(16,20,10,4)(28,40,44,34)
(5,45,11,17)(7,13,9,3)(21,31,41,35)(43,33,23,29)(1,25,15,37)(47,39,19,27) ;
j2 := (6,16,22,14)(8,24,20,4)(38,30,40,46)(2,10,18,12)(28,32,48,44)(34,42,36,26)
(5,31,15,43)(7,45,13,25)(21,19,33,39)(1,35,11,23)(47,41,27,29)(3,17,9,37);
Iso := Group(j1,j2) ; 

# Dep=le groupe isometrie+ du cube (24) Dep = ssg de Iso
d1 := (1,11)(2,18)(3,9)(4,24)(5,15)(6,22)(7,13)(8,20)(10,12)
        (14,16)(17,37)(19,39)(21,33)(23,35)(25,45)(26,42)(27,47)(28,48)(29,41)
        (30,46)(31,43)(32,44)(34,36)(38,40);
d2 := (1,15)(2,22)(3,13)(4,20)(5,11)(6,18)(7,9)(8,24)(10,16)(12,14)
        (17,45)(19,47)(21,41)(23,43)(25,37)(26,46)(27,39)(28,44)(29,33)(30,42)
        (31,35)(32,48)(34,40)(36,38) ;
d3 := (1,17,19)(2,32,10)(3,31,33)(4,40,42)
        (5,45,39)(6,48,12)(7,35,21)(8,34,26)(9,23,29)(11,25,47)(13,43,41)
        (14,22,44)(15,37,27)(16,18,28)(20,38,46)(24,36,30);		
d4 := (1,35,11,23)(2,10,18,12)(3,17,9,37)(4,8,24,20)(5,31,15,43)
        (6,16,22,14)(7,45,13,25)(19,33,39,21)(26,34,42,36)(27,29,47,41)
        (28,32,48,44)(30,40,46,38) ;				
Dep := Group(d1,d2,d3,d4) ;

# Rubik=le groupe du Rubik's Cube		
pH := (2,4,6,8)(26,28,30,32) (1,3,5,7)(17,21,25,29)(19,23,27,31) ;
pB := (18,24,22,20)(42,48,46,44) (9,15,13,11)(33,45,41,37)(35,47,43,39);
pA := (2,34,18,36)(26,10,42,12) (1,35,11,23)(17,9,37,3)(19,33,39,21);
pP := (6,38,22,40)(30,14,46,16) (7,25,13,45)(29,27,41,47)(31,5,43 ,15);
pG := (4,12,20,14)(28,36,44,38) (3,39,13,27)(21,11,41,5)(23,37,43,25);
pD := (8,16,24,10)(32,40,48,34) (1,29,15,33)(17,31,45,35)(19,7,47,9);
Rubik := Group(pH,pB,pA,pP,pG,pD); 

# Pocket=le groupe Pocket (= Rubik sans arêtes)
#pH :=  (1,3,5,7)(17,21,25,29)(19,23,27,31) ;
#pB :=  (9,15,13,11)(33,45,41,37)(35,47,43,39);
#pA :=  (1,35,11,23)(17,9,37,3)(19,33,39,21);
#pP :=  (7,25,13,45)(29,27,41,47)(31,5,43 ,15);
#pG :=  (3,39,13,27)(21,11,41,5)(23,37,43,25);
#pD :=  (1,29,15,33)(17,31,45,35)(19,7,47,9);
#Pocket := Group(pH,pB,pA,pP,pG,pD);

G := Rubik ;;
GG := "Rubik" ;;
J := Iso ;;
JJ := "J" ;;
 
etat := 0 ;;
Jcjg := 0 ;;

    # Les classes des sous groupes conjugaisons de J
    Cl := ConjugacyClassesSubgroups( J );;
    ptfixe := [];

	Print("\n\n No \tetat \tclasses-conjugaisons\n" );
	Print("================================================== \n" );
    # pour toute classe Cl[i], on cherche les pt fixes générés par Cl[i]
    for i  in [Length(Cl),Length(Cl)-1..1]  do

        # prendre un représentant
        H := Representative( Cl[i] );

        # les pt fixes engendrés par H
        aux := Size( Centralizer( G, H ) );

        # si Q inclus dans H,on supprime dans H les pt fixes générés par Q
        for k  in [Length(Cl),Length(Cl)-1..i+1]  do
            for Q  in Elements( Cl[k] )  do
                if IsSubgroup( Q, H )  then
						aux := aux - ptfixe[k];   
                fi;
            od;
        od;

        # sauver les pt fixes génégrés par H
        ptfixe[i] := aux;

        # print N° classe
        Print("\n ", i, ":\t" );

        # le nbr de pt fixes (= nbr états) générés par Cl[i]
        Print( Size(Cl[i]) *  ptfixe[i], "\t" );
		etat := etat + ( Size(Cl[i]) *  ptfixe[i] );

        # le nbr de J-cjg classes générés par Cl[i]
        Print( (Size(Cl[i]) *  ptfixe[i]) /  Index(J,H), " " );
		Jcjg := Jcjg + ( (Size(Cl[i]) *  ptfixe[i] )/  Index(J,H) );
		
    od;
	Print("\n\n ",GG," = ", etat, "\n" );
	Print("\n ",JJ,"-cjg = ", Jcjg , "\n" );