# -*- GAP -*-

d7p_pencil :=
rec(
  graph := [ rec(
          adjacencies := [ [ 8 ], [ 8 ], [ 5 ], [ 5 ], [ 3, 4, 6 ], [ 5, 7 ], [ 6, 8 ], [ 1, 2, 7 ], [ 16 ], [ 16 ], 
              [ 13 ], [ 13 ], [ 11, 12, 14 ], [ 13, 15 ], [ 14, 16 ], [ 9, 10, 15 ], [ 18 ], [ 17 ], [ 20 ], [ 19 ] ],
          autGroup := Group( [ (11,12), ( 9,10), ( 9,11)(10,12)(13,16)(14,15), ( 3, 4), ( 1, 2), 
              ( 1, 3)( 2, 4)( 5, 8)( 6, 7), ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16), (19,20), 
              (17,18), (17,19)(18,20) ] ),
          forms := [ rec(
                  forms := [ [ "[24, 0, 24]" ] ],
                  h := 324 ) ],
          group := Group( [ () ] ),
          h := [ 324 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := -1,
              pencils := [ [ 3, 4 ], [ 2, 4 ], [ 1, 12 ] ],
              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 ],
          order := 20,
          real := [  ],
          representatives := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ],
          schreierVector := [ -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, 
              -20 ] ), rec(
          adjacencies := [ [ 8 ], [ 8 ], [ 5 ], [ 5 ], [ 3, 4, 6 ], [ 5, 7 ], [ 6, 8 ], [ 1, 2, 7 ], [ 10, 20 ], 
              [ 9, 11 ], [ 10, 12 ], [ 11, 13 ], [ 12, 14 ], [ 13, 15 ], [ 14, 16 ], [ 15, 17 ], [ 16, 18 ], 
              [ 17, 19 ], [ 18, 20 ], [ 9, 19 ] ],
          autGroup := Group( [ (10,20)(11,19)(12,18)(13,17)(14,16), ( 9,10)(11,20)(12,19)(13,18)(14,17)(15,16), 
              ( 3, 4), ( 1, 2), ( 1, 3)( 2, 4)( 5, 8)( 6, 7) ] ),
          forms := [ rec(
                  forms := [ [ "[6, 0, 8]" ] ],
                  h := 312 ), rec(
                  forms := [ [ "[2, 0, 6]" ], [ "[2, 1, 2]" ] ],
                  h := 318 ), rec(
                  forms := [ [ "[6, 0, 72]" ] ],
                  h := 320 ), rec(
                  forms := [ [ "[2, 0, 24]" ] ],
                  h := 324 ), rec(
                  forms := [ [ "[6, 0, 18]" ], [ "[6, 3, 6]" ] ],
                  h := 326 ), rec(
                  forms := [ [ "[18, 0, 24]" ] ],
                  h := 332 ) ],
          group := Group( [ () ] ),
          h := [ 312, 318, 320, 324, 326, 332 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := 12,
              pencils := [ [ 3, 2 ], [ 2, 14 ], [ 1, 4 ] ],
              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 ],
          order := 20,
          real := [ 318, 324 ],
          representatives := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ],
          schreierVector := [ -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, 
              -20 ] ) ],
  h := [ 312, 314, 316, 318, 320, 322, 324, 326, 328, 330, 332, 334 ],
  hh := [ rec(
          count := [ 20 ],
          deg := 12,
          h := 312,
          real := [  ] ), rec(
          count := [  ],
          deg := 12,
          h := 314,
          real := [  ] ), rec(
          count := [  ],
          deg := 12,
          h := 316,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 12,
          h := 318,
          real := [ 20 ] ), rec(
          count := [ 20 ],
          deg := 12,
          h := 320,
          real := [  ] ), rec(
          count := [  ],
          deg := 12,
          h := 322,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 12,
          h := 324,
          real := [ 20 ] ), rec(
          count := [ 20 ],
          deg := 12,
          h := 326,
          real := [  ] ), rec(
          count := [  ],
          deg := 12,
          h := 328,
          real := [  ] ), rec(
          count := [  ],
          deg := 12,
          h := 330,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 12,
          h := 332,
          real := [  ] ), rec(
          count := [  ],
          deg := 12,
          h := 334,
          real := [  ] ) ] );

