# -*- GAP -*-

e8p_pencil :=
rec(
  graph := [ rec(
          adjacencies := [ [ 2 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 4, 6 ], [ 5, 7, 9 ], [ 6, 8 ], [ 7 ], [ 6 ], 
              [ 11 ], [ 10, 12 ], [ 11, 13 ], [ 12, 14 ], [ 13, 15 ], [ 14, 16, 18 ], [ 15, 17 ], [ 16 ], [ 15 ], 
              [ 20 ], [ 19 ] ],
          autGroup := Group( [ (19,20), ( 1,10)( 2,11)( 3,12)( 4,13)( 5,14)( 6,15)( 7,16)( 8,17)( 9,18) ] ),
          forms := [ rec(
                  forms := [ [ "[6, 0, 50]", "[14, 6, 24]" ] ],
                  h := 1860 ), rec(
                  forms := [ [ "[18, 9, 42]" ] ],
                  h := 1862 ), rec(
                  forms := [ [ "[6, 3, 14]" ] ],
                  h := 1866 ), rec(
                  forms := [ [ "[6, 0, 18]" ] ],
                  h := 1868 ), rec(
                  forms := [ [ "[2, 0, 150]", "[8, 2, 38]" ] ],
                  h := 1872 ), rec(
                  forms := [ [ "[18, 9, 42]" ] ],
                  h := 1874 ), rec(
                  forms := [ [ "[2, 1, 2]" ] ],
                  h := 1878 ), rec(
                  forms := [ [ "[6, 0, 450]", "[24, 6, 114]" ] ],
                  h := 1880 ), rec(
                  forms := [ [ "[2, 0, 150]", "[8, 2, 38]" ] ],
                  h := 1884 ), rec(
                  forms := [ [ "[6, 3, 114]" ] ],
                  h := 1886 ), rec(
                  forms := [ [ "[6, 3, 14]" ] ],
                  h := 1890 ), rec(
                  forms := [ [ "[18, 0, 150]", "[42, 18, 72]" ] ],
                  h := 1892 ), rec(
                  forms := [ [ "[6, 0, 50]", "[14, 6, 24]" ] ],
                  h := 1896 ), rec(
                  forms := [ [ "[6, 3, 6]" ] ],
                  h := 1898 ), rec(
                  forms := [ [ "[2, 1, 38]" ] ],
                  h := 1902 ), rec(
                  forms := [ [ "[18, 0, 150]", "[42, 18, 72]" ] ],
                  h := 1904 ), rec(
                  forms := [ [ "[2, 0, 6]" ] ],
                  h := 1908 ), rec(
                  forms := [ [ "[6, 3, 114]" ] ],
                  h := 1910 ), rec(
                  forms := [ [ "[2, 1, 38]" ] ],
                  h := 1914 ), rec(
                  forms := [ [ "[6, 0, 450]", "[24, 6, 114]" ] ],
                  h := 1916 ) ],
          group := Group( [ () ] ),
          h := [ 1860, 1862, 1866, 1868, 1872, 1874, 1878, 1880, 1884, 1886, 1890, 1892, 1896, 1898, 1902, 1904, 
              1908, 1910, 1914, 1916 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := -1,
              pencils := [ [ 3, 2 ], [ 2, 10 ], [ 1, 8 ] ],
              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 := [ 1872, 1878, 1884, 1902, 1908, 1914 ],
          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 := [ [ 2 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 4, 6 ], [ 5, 7, 9 ], [ 6, 8 ], [ 7 ], [ 6 ], 
              [ 11 ], [ 10, 12 ], [ 11, 13 ], [ 12, 14 ], [ 13, 15 ], [ 14, 16, 18 ], [ 15, 17 ], [ 16 ], [ 15 ], 
              [  ], [  ] ],
          autGroup := Group( [ ( 1,10)( 2,11)( 3,12)( 4,13)( 5,14)( 6,15)( 7,16)( 8,17)( 9,18), (19,20) ] ),
          forms := [ rec(
                  forms := [ [ "[36, 12, 104]" ] ],
                  h := 1860 ), rec(
                  forms := [ [ "[20, 0, 20]" ], [ "[4, 0, 4]" ] ],
                  h := 1864 ), rec(
                  forms := [ [ "[4, 0, 900]", "[36, 0, 100]" ] ],
                  h := 1868 ), rec(
                  forms := [ [ "[8, 4, 452]", "[68, 32, 68]" ] ],
                  h := 1872 ), rec(
                  forms := [ [ "[8, 4, 52]" ] ],
                  h := 1876 ), rec(
                  forms := [ [ "[4, 0, 900]", "[36, 0, 100]" ] ],
                  h := 1880 ), rec(
                  forms := [ [ "[20, 0, 180]" ], [ "[8, 4, 20]" ] ],
                  h := 1884 ), rec(
                  forms := [ [ "[4, 0, 100]" ] ],
                  h := 1888 ), rec(
                  forms := [ [ "[52, 12, 72]" ] ],
                  h := 1892 ), rec(
                  forms := [ [ "[8, 4, 452]", "[68, 32, 68]" ] ],
                  h := 1896 ), rec(
                  forms := [ [ "[4, 0, 100]" ] ],
                  h := 1900 ), rec(
                  forms := [ [ "[4, 0, 36]" ], [ "[40, 20, 100]" ] ],
                  h := 1904 ), rec(
                  forms := [ [ "[36, 12, 104]" ] ],
                  h := 1908 ), rec(
                  forms := [ [ "[8, 4, 52]" ] ],
                  h := 1912 ), rec(
                  forms := [ [ "[52, 12, 72]" ] ],
                  h := 1916 ) ],
          group := Group( [ () ] ),
          h := [ 1860, 1864, 1868, 1872, 1876, 1880, 1884, 1888, 1892, 1896, 1900, 1904, 1908, 1912, 1916 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := -1,
              pencils := [ [ 3, 2 ], [ 2, 10 ], [ 1, 6 ], [ 0, 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 ],
          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 ] ) ],
  h := [ 1860, 1862, 1864, 1866, 1868, 1870, 1872, 1874, 1876, 1878, 1880, 1882, 1884, 1886, 1888, 1890, 1892, 1894, 
      1896, 1898, 1900, 1902, 1904, 1906, 1908, 1910, 1912, 1914, 1916, 1918 ],
  hh := [ rec(
          count := [ 20 ],
          deg := 30,
          h := 1860,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1862,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1864,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1866,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1868,
          real := [  ] ), rec(
          count := [  ],
          deg := 30,
          h := 1870,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1872,
          real := [ 20 ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1874,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1876,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1878,
          real := [ 20 ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1880,
          real := [  ] ), rec(
          count := [  ],
          deg := 30,
          h := 1882,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1884,
          real := [ 20 ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1886,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1888,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1890,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1892,
          real := [  ] ), rec(
          count := [  ],
          deg := 30,
          h := 1894,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1896,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1898,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1900,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1902,
          real := [ 20 ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1904,
          real := [  ] ), rec(
          count := [  ],
          deg := 30,
          h := 1906,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1908,
          real := [ 20 ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1910,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1912,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1914,
          real := [ 20 ] ), rec(
          count := [ 20 ],
          deg := 30,
          h := 1916,
          real := [  ] ), rec(
          count := [  ],
          deg := 30,
          h := 1918,
          real := [  ] ) ] );

