# -*- GAP -*-

Q54 :=
rec(
  adjacencies := [ [ 8, 10, 14, 18, 20, 22, 24, 29, 31, 33, 36, 37, 50, 51, 52, 53 ], 
      [ 5, 12, 16, 21, 23, 27, 30, 32, 36, 39, 41, 43, 50, 51, 52, 53 ], 
      [ 7, 11, 15, 17, 18, 19, 24, 28, 34, 35, 37, 48, 50, 51, 52, 53 ], 
      [ 13, 15, 16, 20, 21, 26, 29, 34, 44, 49, 50, 52 ], 
      [ 2, 12, 13, 19, 22, 24, 28, 29, 31, 34, 37, 44, 45, 48, 49, 52 ], 
      [ 14, 16, 18, 20, 25, 28, 30, 34, 36, 37, 40, 41, 43, 44, 50, 52 ], 
      [ 3, 11, 20, 21, 22, 23, 26, 27, 29, 36, 39, 40, 41, 44, 45, 52 ], 
      [ 1, 10, 13, 17, 21, 25, 27, 28, 32, 35, 40, 41, 44, 46, 48, 52 ], 
      [ 15, 17, 18, 21, 25, 27, 29, 31, 37, 41, 42, 43, 48, 49, 50, 52 ], 
      [ 1, 8, 15, 16, 19, 23, 26, 30, 34, 39, 42, 43, 45, 49, 52 ], 
      [ 3, 7, 13, 14, 16, 25, 30, 31, 32, 33, 42, 43, 46, 49, 52 ], 
      [ 2, 5, 14, 15, 17, 18, 20, 25, 26, 33, 35, 40, 42, 46, 52 ], 
      [ 4, 5, 8, 11, 18, 23, 33, 35, 36, 37, 41, 43, 45, 47, 51, 53 ], 
      [ 1, 6, 11, 12, 19, 21, 29, 32, 34, 39, 41, 45, 47, 48, 49, 53 ], 
      [ 3, 4, 9, 10, 12, 28, 30, 31, 32, 33, 36, 40, 41, 45, 47, 53 ], 
      [ 2, 4, 6, 10, 11, 17, 22, 27, 31, 35, 37, 40, 46, 47, 48, 53 ], 
      [ 3, 8, 9, 12, 16, 22, 29, 32, 34, 36, 39, 43, 44, 45, 47, 51 ], 
      [ 1, 3, 6, 9, 12, 13, 23, 26, 27, 30, 39, 44, 46, 47, 49 ], 
      [ 3, 5, 10, 14, 21, 25, 26, 27, 31, 35, 36, 40, 43, 44, 47, 50 ], 
      [ 1, 4, 6, 7, 12, 27, 28, 31, 32, 35, 42, 43, 45, 47, 48, 51 ], 
      [ 2, 4, 7, 8, 9, 14, 19, 28, 30, 33, 37, 42, 46, 47, 51 ], 
      [ 1, 5, 7, 16, 17, 25, 26, 28, 30, 33, 41, 42, 47, 49, 50 ], 
      [ 2, 7, 10, 13, 18, 25, 28, 29, 31, 32, 34, 40, 42, 47, 48, 50 ], 
      [ 1, 3, 5, 27, 30, 32, 40, 41, 42, 43, 46, 47 ], [ 6, 8, 9, 11, 12, 19, 22, 23, 38, 45, 51, 53 ], 
      [ 4, 7, 10, 12, 18, 19, 22, 32, 37, 38, 41, 43, 46, 48, 51, 53 ], 
      [ 2, 7, 8, 9, 16, 18, 19, 20, 24, 33, 34, 38, 45, 49, 53 ], 
      [ 3, 5, 6, 8, 15, 20, 21, 22, 23, 38, 39, 43, 46, 49, 53 ], 
      [ 1, 4, 5, 7, 9, 14, 17, 23, 30, 35, 38, 40, 43, 46, 53 ], 
      [ 2, 6, 10, 11, 15, 18, 21, 22, 24, 29, 35, 38, 44, 45, 48, 51 ], 
      [ 1, 5, 9, 11, 15, 16, 19, 20, 23, 38, 39, 41, 44, 46, 51 ], 
      [ 2, 8, 11, 14, 15, 17, 20, 23, 24, 26, 37, 38, 44, 49, 50 ], 
      [ 1, 11, 12, 13, 15, 21, 22, 27, 34, 38, 39, 40, 43, 44, 48, 50 ], 
      [ 3, 4, 5, 6, 10, 14, 17, 23, 27, 33, 38, 41, 42, 46, 51 ], 
      [ 3, 8, 12, 13, 16, 19, 20, 29, 30, 38, 39, 41, 42, 49, 50 ], [ 1, 2, 6, 7, 13, 15, 17, 19, 38, 42, 46, 49 ], 
      [ 1, 3, 5, 6, 9, 13, 16, 21, 26, 32, 38, 39, 40, 42, 45 ], 
      [ 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 47, 52, 54 ], 
      [ 2, 7, 10, 14, 17, 18, 28, 31, 33, 35, 37, 54 ], [ 6, 7, 8, 12, 15, 16, 19, 23, 24, 29, 33, 37, 49, 51, 54 ], 
      [ 2, 6, 7, 8, 9, 13, 14, 15, 22, 24, 26, 31, 34, 35, 54 ], 
      [ 9, 10, 11, 12, 20, 21, 22, 23, 24, 34, 35, 36, 37, 44, 53, 54 ], 
      [ 2, 6, 9, 10, 11, 13, 17, 19, 20, 24, 26, 28, 29, 33, 54 ], 
      [ 4, 5, 6, 7, 8, 17, 18, 19, 30, 31, 32, 33, 42, 53, 54 ], 
      [ 5, 7, 10, 13, 14, 15, 17, 20, 25, 27, 30, 37, 46, 50, 54 ], 
      [ 8, 11, 12, 16, 18, 21, 24, 26, 28, 29, 31, 34, 36, 45, 50, 54 ], 
      [ 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 38, 52, 54 ], [ 3, 5, 8, 9, 14, 16, 20, 23, 26, 30, 33, 54 ], 
      [ 4, 5, 9, 10, 11, 14, 18, 22, 27, 28, 32, 35, 36, 40, 51, 54 ], 
      [ 1, 2, 3, 4, 6, 9, 19, 22, 23, 32, 33, 35, 45, 46, 54 ], 
      [ 1, 2, 3, 13, 17, 20, 21, 25, 26, 30, 31, 34, 40, 49, 54 ], 
      [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 38, 47, 54 ], 
      [ 1, 2, 3, 13, 14, 15, 16, 25, 26, 27, 28, 29, 42, 44, 54 ], 
      [ 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53 ] ],
  autGroup := Group( [ ( 1, 3)( 2,54)( 5,46)( 6, 9)( 7,33)( 8,19)(10,35)(11,22)(12,45)(13,26)(14,17)(15,20)(16,49)
        (18,37)(21,44)(23,38)(27,40)(28,31)(29,34)(30,42)(32,47)(36,48)(41,43)(50,52)(51,53), 
      ( 1,42)( 2,19)( 3,30)( 6, 7)( 8,54)( 9,33)(10,53)(11,18)(12,31)(13,49)(14,23)(16,26)(17,38)(21,50)(22,37)(25,39)
        (27,43)(28,45)(29,34)(32,47)(35,51)(40,41)(44,52), ( 1,38)( 2,17)( 3,23)( 5, 9)( 6,46)( 8,30)(10,35)(11,40)
        (12,43)(13,15)(14,54)(18,28)(19,42)(20,26)(21,44)(22,27)(24,25)(29,52)(31,37)(32,51)(34,50)(41,45)(47,53), 
      ( 1,49)( 2, 7)( 3,16)( 4,24)( 5,20)( 6,19)( 8, 9)(10,18)(11,53)(12,45)(13,42)(15,46)(21,41)(22,51)(26,30)(27,52)
        (28,31)(29,32)(33,54)(34,47)(35,37)(40,50)(43,44) ] ),
  forms := [ rec(
          forms := [ [ "[4, 2, 20]" ] ],
          h := 4 ) ],
  group := Group( [ () ] ),
  h := [ 4 ],
  info := rec(
      bipartite := false,
      distance_regular := false,
      girth := 3,
      pencils := [ [ 16, 24 ], [ 15, 24 ], [ 12, 6 ] ],
      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 ] );

