return [ rec(
      invers := ( 1, 3)( 2, 7)( 4,10)( 5,15)( 6, 8)( 9,11)(12,18)(13,23)(14,16)(17,19)(20,26)(21,31)(22,24)(25,27)
        (28,34)(29,38)(30,32)(33,35)(36,40)(37,39),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 4)( 2,12)( 3, 8)( 5,11)( 6,27)( 7,16)( 9,20)(10,31)(13,19)(14,35)(15,21)(17,23)(18,40)(22,32)
        (24,30)(25,29)(26,37)(28,34)(33,38)(36,39),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 4)( 2,12)( 3, 8)( 5,11)( 6,24)( 7,16)( 9,19)(10,27)(13,18)(14,35)(15,20)(17,23)(21,32)(22,31)
        (25,30)(26,36)(28,34)(29,40)(33,38)(37,39),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 4)( 2,12)( 3, 8)( 5,11)( 6,30)( 7,16)( 9,20)(10,34)(13,19)(14,29)(15,21)(17,27)(18,25)(22,32)
        (23,40)(24,26)(28,33)(31,37)(35,39)(36,38),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 5)( 2,13)( 3,22)( 4, 9)( 6,12)( 7,34)( 8,16)(10,20)(11,38)(14,19)(15,26)(17,31)(18,30)(21,25)
        (23,29)(24,39)(27,33)(28,36)(32,37)(35,40),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 4)( 2,12)( 3, 8)( 5,20)( 6,29)( 7,16)( 9,24)(10,22)(11,21)(13,19)(14,36)(15,25)(17,28)(18,40)
        (23,32)(26,35)(27,33)(30,34)(31,38)(37,39),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 5)( 2,13)( 3,23)( 4, 9)( 6,17)( 7,31)( 8,14)(10,20)(11,40)(12,18)(15,28)(16,27)(19,35)(21,26)
        (22,37)(24,30)(25,33)(29,34)(32,38)(36,39),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 5)( 2,13)( 3,25)( 4, 9)( 6,20)( 7,32)( 8,17)(10,24)(11,40)(12,21)(14,19)(15,36)(16,27)(18,31)
        (22,28)(23,35)(26,30)(29,39)(33,38)(34,37),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 5)( 2,13)( 3,28)( 4, 9)( 6,21)( 7,37)( 8,17)(10,25)(11,33)(12,22)(14,20)(15,23)(16,32)(18,39)
        (19,35)(24,38)(26,31)(27,30)(29,34)(36,40),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 5)( 2,12)( 3,26)( 4, 9)( 6,20)( 7,37)( 8,16)(10,24)(11,21)(13,19)(14,36)(15,30)(17,34)(18,33)
        (22,28)(23,38)(25,29)(27,32)(31,39)(35,40),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 5)( 2,13)( 3,27)( 4, 9)( 6,21)( 7,36)( 8,17)(10,25)(11,32)(12,22)(14,20)(15,39)(16,30)(18,35)
        (19,34)(23,31)(24,38)(26,29)(28,33)(37,40),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 5)( 2,13)( 3,24)( 4, 9)( 6,17)( 7,23)( 8,14)(10,20)(11,19)(12,18)(15,32)(16,28)(21,27)(22,33)
        (25,31)(26,40)(29,38)(30,36)(34,39)(35,37),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 5)( 2,12)( 3,25)( 4, 9)( 6,19)( 7,24)( 8,16)(10,21)(11,20)(13,18)(14,36)(15,29)(17,33)(22,28)
        (23,34)(26,32)(27,40)(30,38)(31,37)(35,39),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 5)( 2,13)( 3,10)( 4, 9)( 6,12)( 7,25)( 8,17)(11,16)(14,20)(15,26)(18,21)(19,29)(22,28)(23,38)
        (24,33)(27,32)(30,35)(31,39)(34,36)(37,40),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 5)( 2,13)( 3,10)( 4, 9)( 6,12)( 7,24)( 8,17)(11,21)(14,20)(15,29)(16,22)(18,25)(19,33)(23,26)
        (27,32)(28,36)(30,35)(31,40)(34,38)(37,39),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 5)( 2,13)( 3,10)( 4, 9)( 6,21)( 7,30)( 8,17)(11,24)(12,22)(14,20)(15,38)(16,25)(18,28)(19,39)
        (23,34)(26,37)(27,35)(29,33)(31,36)(32,40),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 5)( 2,13)( 3,10)( 4, 9)( 6,21)( 7,29)( 8,17)(11,24)(12,22)(14,20)(15,40)(16,25)(18,28)(19,37)
        (23,32)(26,35)(27,33)(30,34)(31,38)(36,39),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 5)( 2,13)( 3,10)( 4, 9)( 6,21)( 7,26)( 8,17)(11,23)(12,22)(14,20)(15,31)(16,24)(18,27)(19,35)
        (25,28)(29,34)(30,38)(32,37)(33,39)(36,40),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 5)( 2,13)( 3,23)( 4, 9)( 6,12)( 7,32)( 8,18)(10,19)(11,35)(14,17)(15,31)(16,27)(20,26)(21,40)
        (22,36)(24,30)(25,29)(28,38)(33,37)(34,39),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 5)( 2,14)( 3,23)( 4,10)( 6,13)( 7,25)( 8,18)( 9,11)(12,22)(15,21)(16,34)(17,26)(19,28)(20,37)
        (24,29)(27,30)(31,36)(32,39)(33,38)(35,40),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 5)( 2,14)( 3,23)( 4,10)( 6,13)( 7,25)( 8,18)( 9,11)(12,22)(15,21)(16,34)(17,26)(19,28)(20,38)
        (24,29)(27,30)(31,37)(32,36)(33,39)(35,40),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 5)( 2,15)( 3,24)( 4,10)( 6,14)( 7,34)( 8,19)( 9,11)(12,23)(13,38)(16,22)(17,21)(18,27)(20,31)
        (25,30)(26,39)(28,33)(29,36)(32,37)(35,40),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 3)( 2,12)( 4,10)( 5,29)( 6,16)( 7,11)( 8,19)( 9,30)(13,15)(14,20)(17,26)(18,23)(21,25)(22,33)
        (24,37)(27,32)(28,38)(31,36)(34,40)(35,39),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 3)( 2,12)( 4,10)( 5,30)( 6,16)( 7,11)( 8,19)( 9,31)(13,15)(14,20)(17,27)(18,23)(21,26)(22,34)
        (24,38)(25,37)(28,33)(29,39)(32,36)(35,40),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 3)( 2,12)( 4,10)( 5,31)( 6,16)( 7,11)( 8,19)( 9,34)(13,15)(14,23)(17,30)(18,26)(20,25)(21,40)
        (22,35)(24,29)(27,38)(28,37)(32,36)(33,39),
      nbP := 40,
      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) ), rec(
      invers := ( 1, 3)( 2,39)( 4,35)( 5,40)( 6,10)( 7,12)( 8,17)( 9,14)(11,13)(15,21)(16,18)(19,25)(20,22)(23,29)
        (24,26)(27,33)(28,30)(31,37)(32,34)(36,38),
      nbP := 40,
      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) ) ];
