# -*- GAP -*-

e7p_pencil :=
rec(
  graph := [ rec(
          adjacencies := [ [ 2 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5, 7 ], [ 4, 6 ], [ 5, 8 ], [ 4 ], [ 6 ], [ 10 ], 
              [ 9, 11 ], [ 10, 12 ], [ 11, 13, 15 ], [ 12, 14 ], [ 13, 16 ], [ 12 ], [ 14 ], [ 20 ], [ 20 ], [ 20 ], 
              [ 17, 18, 19 ] ],
          autGroup := Group( [ ( 1, 8)( 2, 6)( 3, 5), ( 9,16)(10,14)(11,13), ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)
                ( 6,14)( 7,15)( 8,16), (18,19), (17,18) ] ),
          forms := [ rec(
                  forms := [ [ "[8, 4, 164]", "[20, 8, 68]" ] ],
                  h := 684 ), rec(
                  forms := [ [ "[4, 0, 324]", "[36, 12, 40]" ] ],
                  h := 692 ), rec(
                  forms := [ [ "[8, 4, 164]", "[20, 8, 68]" ] ],
                  h := 696 ), rec(
                  forms := [ [ "[4, 0, 324]", "[36, 12, 40]" ] ],
                  h := 704 ), rec(
                  forms := [ [ "[8, 4, 164]", "[20, 8, 68]" ] ],
                  h := 708 ), rec(
                  forms := [ [ "[4, 0, 36]" ], [ "[4, 0, 4]" ], [ "[8, 4, 20]" ] ],
                  h := 712 ), rec(
                  forms := [ [ "[4, 0, 324]", "[36, 12, 40]" ] ],
                  h := 716 ) ],
          group := Group( [ () ] ),
          h := [ 684, 692, 696, 704, 708, 712, 716 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := -1,
              pencils := [ [ 3, 3 ], [ 2, 8 ], [ 1, 9 ] ],
              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 := [ [ 2 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5, 7 ], [ 4, 6 ], [ 5, 8 ], [ 4 ], [ 6 ], [ 10 ], 
              [ 9, 11 ], [ 10, 12 ], [ 11, 13, 15 ], [ 12, 14 ], [ 13, 16 ], [ 12 ], [ 14 ], [ 18 ], [ 17, 19 ], 
              [ 18, 20 ], [ 19 ] ],
          autGroup := Group( [ (17,20)(18,19), ( 9,16)(10,14)(11,13), ( 1, 8)( 2, 6)( 3, 5), 
              ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16) ] ),
          forms := [ rec(
                  forms := [ [ "[20, 0, 324]", "[56, 4, 116]" ] ],
                  h := 684 ), rec(
                  forms := [ [ "[4, 0, 1620]", "[36, 12, 184]" ] ],
                  h := 688 ), rec(
                  forms := [ [ "[24, 12, 276]" ] ],
                  h := 692 ), rec(
                  forms := [ [ "[20, 0, 324]", "[56, 4, 116]" ] ],
                  h := 696 ), rec(
                  forms := [ [ "[4, 0, 1620]", "[36, 12, 184]" ] ],
                  h := 700 ), rec(
                  forms := [ [ "[84, 24, 84]" ] ],
                  h := 704 ), rec(
                  forms := [ [ "[20, 0, 324]", "[56, 4, 116]" ] ],
                  h := 708 ), rec(
                  forms := [ [ "[4, 0, 1620]", "[36, 12, 184]" ] ],
                  h := 712 ), rec(
                  forms := [ [ "[20, 0, 36]" ], [ "[24, 12, 36]" ], [ "[36, 0, 180]" ], [ "[4, 0, 180]" ], 
                      [ "[4, 0, 20]" ] ],
                  h := 716 ) ],
          group := Group( [ () ] ),
          h := [ 684, 688, 692, 696, 700, 704, 708, 712, 716 ],
          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 := [  ],
          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, 7 ], [ 4, 6 ], [ 5, 8 ], [ 4 ], [ 6 ], [ 10 ], 
              [ 9, 11 ], [ 10, 12 ], [ 11, 13, 15 ], [ 12, 14 ], [ 13, 16 ], [ 12 ], [ 14 ], [ 18 ], [ 17, 19 ], 
              [ 18 ], [  ] ],
          autGroup := Group( [ ( 9,16)(10,14)(11,13), ( 1, 8)( 2, 6)( 3, 5), ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)
                ( 6,14)( 7,15)( 8,16), (17,19) ] ),
          forms := [ rec(
                  forms := [ [ "[8, 0, 324]", "[44, 20, 68]" ] ],
                  h := 684 ), rec(
                  forms := [ [ "[4, 0, 648]", "[36, 12, 76]" ] ],
                  h := 688 ), rec(
                  forms := [ [ "[24, 0, 108]" ] ],
                  h := 692 ), rec(
                  forms := [ [ "[8, 0, 324]", "[44, 20, 68]" ] ],
                  h := 696 ), rec(
                  forms := [ [ "[4, 0, 648]", "[36, 12, 76]" ] ],
                  h := 700 ), rec(
                  forms := [ [ "[12, 0, 216]" ] ],
                  h := 704 ), rec(
                  forms := [ [ "[8, 0, 324]", "[44, 20, 68]" ] ],
                  h := 708 ), rec(
                  forms := [ [ "[4, 0, 648]", "[36, 12, 76]" ] ],
                  h := 712 ), rec(
                  forms := [ [ "[12, 0, 24]" ], [ "[36, 0, 72]" ], [ "[4, 0, 72]" ], [ "[4, 0, 8]" ], 
                      [ "[8, 0, 36]" ] ],
                  h := 716 ) ],
          group := Group( [ () ] ),
          h := [ 684, 688, 692, 696, 700, 704, 708, 712, 716 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := -1,
              pencils := [ [ 3, 2 ], [ 2, 9 ], [ 1, 8 ], [ 0, 1 ] ],
              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 := [ [ 2 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5, 7 ], [ 4, 6 ], [ 5, 8 ], [ 4 ], [ 6 ], [ 10 ], 
              [ 9, 11 ], [ 10, 12 ], [ 11, 13, 15 ], [ 12, 14 ], [ 13, 16 ], [ 12 ], [ 14 ], [ 18 ], [ 17 ], [ 20 ], 
              [ 19 ] ],
          autGroup := Group( [ ( 1, 8)( 2, 6)( 3, 5), ( 9,16)(10,14)(11,13), ( 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, 12, 60]" ] ],
                  h := 692 ), rec(
                  forms := [ [ "[12, 0, 12]" ] ],
                  h := 704 ), rec(
                  forms := [ [ "[12, 0, 108]" ] ],
                  h := 716 ) ],
          group := Group( [ () ] ),
          h := [ 692, 704, 716 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := -1,
              pencils := [ [ 3, 2 ], [ 2, 8 ], [ 1, 10 ] ],
              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 := [ [ 2 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5, 7 ], [ 4, 6 ], [ 5, 8 ], [ 4 ], [ 6 ], [ 10 ], 
              [ 9, 11 ], [ 10, 12 ], [ 11, 13, 15 ], [ 12, 14 ], [ 13, 16 ], [ 12 ], [ 14 ], [  ], [  ], [  ], [  ] ],
          autGroup := Group( [ ( 1, 8)( 2, 6)( 3, 5), ( 9,16)(10,14)(11,13), ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)
                ( 6,14)( 7,15)( 8,16), (19,20), (18,19), (17,18) ] ),
          forms := [ rec(
                  forms := [ [ "[8, 4, 164]", "[20, 8, 68]" ] ],
                  h := 684 ), rec(
                  forms := [ [ "[4, 0, 36]" ], [ "[4, 0, 4]" ], [ "[8, 4, 20]" ] ],
                  h := 688 ), rec(
                  forms := [ [ "[4, 0, 324]", "[36, 12, 40]" ] ],
                  h := 692 ), rec(
                  forms := [ [ "[8, 4, 164]", "[20, 8, 68]" ] ],
                  h := 696 ), rec(
                  forms := [ [ "[4, 0, 324]", "[36, 12, 40]" ] ],
                  h := 704 ), rec(
                  forms := [ [ "[8, 4, 164]", "[20, 8, 68]" ] ],
                  h := 708 ), rec(
                  forms := [ [ "[4, 0, 324]", "[36, 12, 40]" ] ],
                  h := 716 ) ],
          group := Group( [ () ] ),
          h := [ 684, 688, 692, 696, 704, 708, 716 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := -1,
              pencils := [ [ 3, 2 ], [ 2, 8 ], [ 1, 6 ], [ 0, 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 := [  ],
          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, 7 ], [ 4, 6 ], [ 5, 8 ], [ 4 ], [ 6 ], [ 19 ], [ 19 ], 
              [ 13 ], [ 13 ], [ 11, 12, 14 ], [ 13, 15 ], [ 14, 16 ], [ 15, 17 ], [ 16, 18 ], [ 17, 19 ], 
              [ 9, 10, 18 ], [  ] ],
          autGroup := Group( [ ( 1, 8)( 2, 6)( 3, 5), (11,12), ( 9,10), ( 9,11)(10,12)(13,19)(14,18)(15,17) ] ),
          forms := [ rec(
                  forms := [ [ "[8, 4, 164]", "[20, 8, 68]" ] ],
                  h := 684 ), rec(
                  forms := [ [ "[4, 0, 324]", "[36, 12, 40]" ] ],
                  h := 692 ), rec(
                  forms := [ [ "[8, 4, 164]", "[20, 8, 68]" ] ],
                  h := 696 ), rec(
                  forms := [ [ "[4, 0, 324]", "[36, 12, 40]" ] ],
                  h := 704 ), rec(
                  forms := [ [ "[8, 4, 164]", "[20, 8, 68]" ] ],
                  h := 708 ), rec(
                  forms := [ [ "[4, 0, 36]" ], [ "[4, 0, 4]" ], [ "[8, 4, 20]" ] ],
                  h := 712 ), rec(
                  forms := [ [ "[4, 0, 324]", "[36, 12, 40]" ] ],
                  h := 716 ) ],
          group := Group( [ () ] ),
          h := [ 684, 692, 696, 704, 708, 712, 716 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := -1,
              pencils := [ [ 3, 3 ], [ 2, 9 ], [ 1, 7 ], [ 0, 1 ] ],
              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 := [ 684, 686, 688, 690, 692, 694, 696, 698, 700, 702, 704, 706, 708, 710, 712, 714, 716, 718 ],
  hh := [ rec(
          count := [ 20 ],
          deg := 18,
          h := 684,
          real := [  ] ), rec(
          count := [  ],
          deg := 18,
          h := 686,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 18,
          h := 688,
          real := [  ] ), rec(
          count := [  ],
          deg := 18,
          h := 690,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 18,
          h := 692,
          real := [  ] ), rec(
          count := [  ],
          deg := 18,
          h := 694,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 18,
          h := 696,
          real := [  ] ), rec(
          count := [  ],
          deg := 18,
          h := 698,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 18,
          h := 700,
          real := [  ] ), rec(
          count := [  ],
          deg := 18,
          h := 702,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 18,
          h := 704,
          real := [  ] ), rec(
          count := [  ],
          deg := 18,
          h := 706,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 18,
          h := 708,
          real := [  ] ), rec(
          count := [  ],
          deg := 18,
          h := 710,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 18,
          h := 712,
          real := [  ] ), rec(
          count := [  ],
          deg := 18,
          h := 714,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 18,
          h := 716,
          real := [  ] ), rec(
          count := [  ],
          deg := 18,
          h := 718,
          real := [  ] ) ] );

