# -*- GAP -*-

X54 :=
rec(
  adjacencies := [ [ 9, 13, 15, 17, 18, 27, 33, 35, 36, 39, 42, 45, 48, 49, 50, 51, 52, 53 ], 
      [ 17, 21, 22, 24, 28, 30, 32, 35, 36, 39, 43, 47, 51, 53 ], 
      [ 17, 20, 22, 24, 29, 30, 32, 35, 36, 39, 43, 47, 50, 52 ], 
      [ 10, 11, 16, 18, 19, 20, 21, 25, 28, 29, 33, 34, 36, 39, 43, 47, 48, 49 ], 
      [ 18, 20, 22, 23, 29, 30, 31, 33, 36, 39, 44, 46, 51, 53 ], 
      [ 18, 21, 22, 23, 28, 30, 31, 33, 36, 39, 44, 46, 50, 52 ], 
      [ 8, 12, 14, 17, 19, 20, 21, 26, 28, 29, 34, 35, 36, 39, 44, 46, 48, 49 ], 
      [ 7, 12, 18, 22, 23, 25, 27, 32, 36, 40, 42, 47, 50, 51 ], 
      [ 1, 13, 19, 20, 21, 23, 24, 25, 26, 30, 36, 40, 43, 46 ], 
      [ 4, 11, 17, 22, 24, 26, 27, 31, 36, 40, 44, 45, 52, 53 ], 
      [ 4, 10, 14, 15, 23, 30, 32, 35, 36, 41, 42, 46, 50, 51 ], 
      [ 7, 8, 15, 16, 24, 30, 31, 33, 36, 41, 43, 45, 52, 53 ], 
      [ 1, 9, 14, 16, 22, 28, 29, 31, 32, 34, 36, 41, 44, 47 ], 
      [ 7, 11, 13, 18, 24, 26, 30, 31, 37, 39, 42, 47, 52, 53 ], 
      [ 1, 11, 12, 19, 22, 27, 28, 29, 31, 32, 37, 39, 43, 46 ], 
      [ 4, 12, 13, 17, 23, 25, 30, 32, 37, 39, 44, 45, 50, 51 ], [ 1, 2, 3, 7, 10, 16, 23, 31, 33, 34, 37, 40, 42, 46 
         ], [ 1, 4, 5, 6, 8, 14, 24, 32, 34, 35, 37, 40, 43, 45 ], 
      [ 4, 7, 9, 15, 22, 30, 33, 35, 37, 40, 44, 47, 50, 51, 52, 53 ], 
      [ 3, 4, 5, 7, 9, 27, 31, 32, 37, 41, 42, 45, 51, 52 ], [ 2, 4, 6, 7, 9, 27, 31, 32, 37, 41, 42, 45, 50, 53 ], 
      [ 2, 3, 5, 6, 8, 10, 13, 15, 19, 25, 26, 34, 37, 41, 42, 45, 48, 49 ], 
      [ 5, 6, 8, 9, 11, 16, 17, 26, 27, 28, 29, 35, 37, 41, 43, 47, 48, 49, 52, 53 ], 
      [ 2, 3, 9, 10, 12, 14, 18, 25, 27, 28, 29, 33, 37, 41, 44, 46, 48, 49, 50, 51 ], 
      [ 4, 8, 9, 16, 22, 24, 31, 35, 38, 39, 42, 46, 52, 53 ], [ 7, 9, 10, 14, 22, 23, 32, 33, 38, 39, 43, 45, 50, 51 
         ], [ 1, 8, 10, 15, 20, 21, 23, 24, 30, 34, 38, 39, 44, 47 ], 
      [ 2, 4, 6, 7, 13, 15, 23, 24, 38, 40, 42, 45, 51, 52 ], [ 3, 4, 5, 7, 13, 15, 23, 24, 38, 40, 42, 45, 50, 53 ], 
      [ 2, 3, 5, 6, 9, 11, 12, 14, 16, 19, 27, 34, 38, 40, 42, 45, 48, 49 ], 
      [ 5, 6, 10, 12, 13, 14, 15, 17, 20, 21, 25, 35, 38, 40, 43, 47, 48, 49, 50, 51 ], 
      [ 2, 3, 8, 11, 13, 15, 16, 18, 20, 21, 26, 33, 38, 40, 44, 46, 48, 49, 52, 53 ], 
      [ 1, 4, 5, 6, 12, 17, 19, 24, 26, 32, 38, 41, 42, 47 ], 
      [ 4, 7, 13, 17, 18, 22, 27, 30, 38, 41, 43, 46, 50, 51, 52, 53 ], 
      [ 1, 2, 3, 7, 11, 18, 19, 23, 25, 31, 38, 41, 44, 45 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 37, 38, 54 
         ], [ 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 36, 38, 54 ], 
      [ 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 54 ], 
      [ 1, 2, 3, 4, 5, 6, 7, 14, 15, 16, 25, 26, 27, 40, 41, 54 ], 
      [ 8, 9, 10, 17, 18, 19, 28, 29, 30, 31, 32, 39, 41, 54 ], 
      [ 11, 12, 13, 20, 21, 22, 23, 24, 33, 34, 35, 39, 40, 54 ], 
      [ 1, 8, 11, 14, 17, 20, 21, 22, 25, 28, 29, 30, 33, 43, 44, 54 ], 
      [ 2, 3, 4, 9, 12, 15, 18, 23, 26, 31, 34, 42, 44, 54 ], [ 5, 6, 7, 10, 13, 16, 19, 24, 27, 32, 35, 42, 43, 54 ],
      [ 1, 10, 12, 16, 18, 20, 21, 22, 26, 28, 29, 30, 35, 46, 47, 54 ], 
      [ 5, 6, 7, 9, 11, 15, 17, 24, 25, 32, 34, 45, 47, 54 ], [ 2, 3, 4, 8, 13, 14, 19, 23, 27, 31, 33, 45, 46, 54 ], 
      [ 1, 4, 7, 22, 23, 24, 30, 31, 32, 54 ], [ 1, 4, 7, 22, 23, 24, 30, 31, 32, 54 ], 
      [ 1, 3, 6, 8, 11, 16, 19, 21, 24, 26, 29, 31, 34, 54 ], [ 1, 2, 5, 8, 11, 16, 19, 20, 24, 26, 28, 31, 34, 54 ], 
      [ 1, 3, 6, 10, 12, 14, 19, 20, 23, 25, 28, 32, 34, 54 ], [ 1, 2, 5, 10, 12, 14, 19, 21, 23, 25, 29, 32, 34, 54 ]
        , [ 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53 ] ],
  autGroup := Group( [ ( 8,14)( 9,15)(10,16)(11,25)(12,26)(13,27)(20,29)(21,28)(22,30)(23,31)(24,32)(36,39)(37,40)
        (38,41)(50,52)(51,53), ( 1, 7)( 4,54)( 5, 6)( 8,27)( 9,26)(10,40)(11,41)(12,15)(13,14)(16,37)(18,44)(19,45)
        (20,50)(21,51)(22,30)(24,32)(25,38)(28,53)(29,52)(33,46)(34,42)(36,39), ( 8,26)( 9,27)(10,25)(11,16)(12,14)
        (13,15)(17,35)(18,33)(19,34)(36,39)(37,41)(38,40)(42,45)(43,47)(44,46), ( 1,54)( 4, 7)( 8,11)( 9,37)(10,12)
        (13,38)(14,25)(15,40)(16,26)(17,43)(18,46)(22,30)(27,41)(33,44)(35,47), ( 2, 3)( 5, 6)(20,21)(28,29)(50,51)
        (52,53), ( 2, 5)( 3, 6)( 4, 7)( 8,10)(11,12)(14,16)(17,18)(20,21)(23,24)(25,26)(28,29)(31,32)(33,35)(42,45)
        (43,46)(44,47)(50,52)(51,53), ( 2,20)( 3,21)( 4,22)( 5,28)( 6,29)( 7,30)( 8,11)( 9,17)(10,25)(12,14)(13,33)
        (15,18)(16,26)(19,34)(24,31)(27,35)(36,42)(37,43)(38,44)(39,45)(40,46)(41,47)(52,53), (48,49) ] ),
  forms := [ rec(
          forms := [ [ "[4, 0, 24]" ] ],
          h := 4 ) ],
  group := Group( [ () ] ),
  h := [ 4 ],
  info := rec(
      bipartite := false,
      distance_regular := false,
      girth := 3,
      pencils := [ [ 20, 4 ], [ 18, 6 ], [ 16, 6 ], [ 14, 36 ], [ 10, 2 ] ],
      regular := false,
      transitive := -1 ),
  isGraph := true,
  isSimple := true,
  names := [ 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 ],
  order := 54,
  real := [  ],
  representatives := [ 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 ]
   ,
  schreierVector := [ -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 ] );

