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