# -*- GAP -*-

Phi25 :=
rec(
  adjacencies := [ [ 2, 5, 21 ], [ 1, 3, 22 ], [ 2, 4, 23 ], [ 3, 5, 24 ], [ 1, 4, 25 ], [ 7, 10, 21 ], [ 6, 8, 22 ], 
      [ 7, 9, 23 ], [ 8, 10, 24 ], [ 6, 9, 25 ], [ 12, 15, 21 ], [ 11, 13, 24 ], [ 12, 14, 22 ], [ 13, 15, 25 ], 
      [ 11, 14, 23 ], [ 17, 20, 21 ], [ 16, 18, 24 ], [ 17, 19, 22 ], [ 18, 20, 25 ], [ 16, 19, 23 ], 
      [ 1, 6, 11, 16 ], [ 2, 7, 13, 18 ], [ 3, 8, 15, 20 ], [ 4, 9, 12, 17 ], [ 5, 10, 14, 19 ] ],
  autGroup := Group( [ (11,16)(12,17)(13,18)(14,19)(15,20), ( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)
        (22,25)(23,24), ( 1, 2)( 3, 5)( 6, 7)( 8,10)(11,13)(14,15)(16,18)(19,20)(21,22)(23,25), 
      ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10), ( 1,11)( 2,12, 5,15)( 3,13, 4,14)( 6,16)( 7,17,10,20)( 8,18, 9,19)
        (22,24,25,23) ] ),
  forms := [ rec(
          forms := [ [ "U(5) + [16]" ] ],
          h := 4 ), rec(
          forms := [ [ "[-10] + [6, 1, 6]", "U(5) + [14]" ] ],
          h := 6 ), rec(
          forms := [ [ "[-20] + [2, 1, 8]", "U(5) + [12]" ] ],
          h := 8 ), rec(
          forms := [ [ "U(5) + [10]" ] ],
          h := 10 ), rec(
          forms := [ [ "U(5) + [8]" ] ],
          h := 12 ), rec(
          forms := [ [ "[-10] + [4, 1, 4]", "U(5) + [6]" ] ],
          h := 14 ), rec(
          forms := [ [ "U(5) + [4]" ] ],
          h := 16 ), rec(
          forms := [ [ "U(5) + [2]" ] ],
          h := 18 ), rec(
          forms := [ [ "U(1) + U(5)" ] ],
          h := 20 ) ],
  group := Group( [ () ] ),
  h := [ 4, 6, 8, 10, 12, 14, 16, 18, 20 ],
  info := rec(
      bipartite := false,
      distance_regular := false,
      girth := 5,
      pencils := [ [ 4, 5 ], [ 3, 20 ] ],
      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 ],
  order := 25,
  real := [ 8, 12, 18, 20 ],
  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 ],
  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 ] );

