return [ rec(
      invers := ( 1, 5)( 2,13)( 3,29)( 4, 9)( 6,21)( 7,41)( 8,17)(10,25)(11,49)(12,22)(14,20)(15,62)(16,33)(18,37)
        (19,59)(23,46)(24,45)(26,32)(27,67)(28,53)(30,36)(31,72)(34,57)(35,69)(38,44)(39,73)(40,63)(42,48)(43,77)
        (47,52)(50,56)(51,78)(54,64)(55,76)(58,61)(60,66)(65,70)(68,71)(74,80)(75,79),
      nbP := 80,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59,60)
        (61,62)(63,64,65,66)(67,68,69,70)(71,72)(73,74,75,76)(77,78,79,80) ), rec(
      invers := ( 1, 5)( 2,13)( 3,29)( 4, 9)( 6,21)( 7,42)( 8,17)(10,25)(11,34)(12,22)(14,20)(15,23)(16,33)(18,38)
        (19,37)(24,40)(26,32)(27,51)(28,43)(30,36)(31,55)(35,46)(39,41)(44,47)(45,56)(48,54)(49,67)(50,59)(52,58)
        (53,71)(57,62)(60,63)(61,72)(64,70)(65,76)(66,75)(68,74)(69,80)(73,78)(77,79),
      nbP := 80,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)
        (59,60,61,62)(63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80) ), rec(
      invers := ( 1, 5)( 2,13)( 3,27)( 4, 9)( 6,21)( 7,39)( 8,17)(10,25)(11,51)(12,22)(14,20)(15,59)(16,31)(18,36)
        (19,35)(23,47)(24,43)(26,30)(28,34)(29,52)(32,55)(33,68)(37,42)(38,60)(40,46)(41,76)(44,63)(45,80)(48,54)
        (49,72)(50,64)(53,67)(56,62)(57,65)(58,71)(61,75)(66,78)(69,74)(70,73)(77,79),
      nbP := 80,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26)(27,28,29,30)
        (31,32,33,34)(35,36,37,38)(39,40,41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80) ), rec(
      invers := ( 1, 5)( 2,13)( 3,29)( 4, 9)( 6,21)( 7,39)( 8,17)(10,25)(11,47)(12,22)(14,20)(15,56)(16,34)(18,35)
        (19,59)(23,44)(24,43)(26,32)(27,67)(28,51)(30,33)(31,55)(36,42)(37,71)(38,63)(40,46)(41,75)(45,50)(48,54)
        (49,76)(52,64)(53,74)(57,62)(58,68)(60,66)(61,80)(65,70)(69,79)(72,78)(73,77),
      nbP := 80,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34)(35,36,37,38)(39,40,41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)
        (59,60,61,62)(63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80) ), rec(
      invers := ( 1, 5)( 2,13)( 3,27)( 4, 9)( 6,19)( 7,35)( 8,15)(10,23)(11,47)(12,20)(14,18)(16,31)(17,28)(21,43)
        (22,39)(24,30)(25,67)(26,51)(29,55)(32,38)(33,73)(34,56)(36,42)(37,77)(40,60)(41,59)(44,50)(45,66)(46,61)
        (48,54)(49,53)(52,63)(57,71)(58,68)(62,78)(64,70)(65,79)(69,75)(72,76)(74,80),
      nbP := 80,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14)(15,16,17,18)(19,20,21,22)(23,24,25,26)(27,28,29,30)
        (31,32,33,34)(35,36,37,38)(39,40,41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72)(73,74,75,76)(77,78,79,80) ), rec(
      invers := ( 1, 5)( 2,13)( 3,29)( 4, 9)( 6,21)( 7,41)( 8,17)(10,26)(11,25)(12,22)(14,20)(15,57)(16,33)(18,37)
        (19,61)(23,49)(24,45)(27,32)(28,50)(30,36)(31,70)(34,53)(35,73)(38,44)(39,79)(40,66)(42,48)(43,75)(46,67)
        (47,72)(51,69)(52,68)(54,60)(55,59)(56,77)(58,64)(62,65)(63,78)(71,76)(74,80),
      nbP := 80,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)
        (29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59,60)
        (61,62,63,64)(65,66)(67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80) ), rec(
      invers := ( 1, 5)( 2,15)( 3,80)( 4,10)( 6,14)( 7,27)( 8,19)( 9,11)(12,79)(13,18)(16,22)(17,28)(20,23)(21,31)
        (24,30)(25,43)(26,35)(29,34)(32,38)(33,44)(36,39)(37,47)(40,46)(41,59)(42,51)(45,50)(48,54)(49,60)(52,55)
        (53,63)(56,62)(57,75)(58,67)(61,66)(64,70)(65,76)(68,72)(69,71)(73,78)(74,77),
      nbP := 80,
      next := ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10)(11,12,13,14)(15,16,17,18)(19,20,21,22)(23,24,25,26)(27,28,29,30)
        (31,32,33,34)(35,36,37,38)(39,40,41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80) ), rec(
      invers := ( 1, 3)( 2, 4)( 5,10)( 6, 7)( 8,11)( 9,12)(13,18)(14,15)(16,19)(17,20)(21,26)(22,23)(24,27)(25,28)
        (29,34)(30,31)(32,35)(33,36)(37,42)(38,39)(40,43)(41,44)(45,50)(46,47)(48,51)(49,52)(53,58)(54,55)(56,59)
        (57,60)(61,66)(62,63)(64,67)(65,68)(69,74)(70,71)(72,75)(73,76)(77,80)(78,79),
      nbP := 80,
      next := ( 1, 2)( 3, 4, 5, 6)( 7, 8, 9,10)(11,12,13,14)(15,16,17,18)(19,20,21,22)(23,24,25,26)(27,28,29,30)
        (31,32,33,34)(35,36,37,38)(39,40,41,42)(43,44,45,46)(47,48,49,50)(51,52,53,54)(55,56,57,58)(59,60,61,62)
        (63,64,65,66)(67,68,69,70)(71,72,73,74)(75,76,77,78)(79,80) ) ];
