# -*- GAP -*-

a6p_pencil :=
rec(
  graph := [ rec(
          adjacencies := [ [ 2, 7 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 4, 6 ], [ 5, 7 ], [ 1, 6 ], [ 9, 14 ], 
              [ 8, 10 ], [ 9, 11 ], [ 10, 12 ], [ 11, 13 ], [ 12, 14 ], [ 8, 13 ], [ 16, 21 ], [ 15, 17 ], 
              [ 16, 18 ], [ 17, 19 ], [ 18, 20 ], [ 19, 21 ], [ 15, 20 ] ],
          autGroup := Group( [ (16,21)(17,20)(18,19), (15,16)(17,21)(18,20), ( 9,14)(10,13)(11,12), 
              ( 8, 9)(10,14)(11,13), ( 8,15)( 9,16)(10,17)(11,18)(12,19)(13,20)(14,21), ( 2, 7)( 3, 6)( 4, 5), 
              ( 1, 2)( 3, 7)( 4, 6), ( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14) ] ),
          forms := [ rec(
                  forms := [ [ "[2, 1, 4]" ] ],
                  h := 112 ), rec(
                  forms := [ [ "[14, 7, 28]" ] ],
                  h := 114 ), rec(
                  forms := [ [ "[14, 7, 28]" ] ],
                  h := 116 ), rec(
                  forms := [ [ "[14, 7, 28]" ] ],
                  h := 120 ) ],
          group := Group( [ () ] ),
          h := [ 112, 114, 116, 120 ],
          info := rec(
              bipartite := false,
              distance_regular := false,
              girth := 7,
              pencils := [ [ 2, 21 ] ],
              regular := 2,
              transitive := 6 ),
          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 ],
          order := 21,
          real := [ 112 ],
          representatives := [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 ],
          schreierVector := [ -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, 
              -20, -21 ] ), rec(
          adjacencies := [ [ 2, 7 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 4, 6 ], [ 5, 7 ], [ 1, 6 ], [ 9, 14 ], 
              [ 8, 10 ], [ 9, 11 ], [ 10, 12 ], [ 11, 13 ], [ 12, 14 ], [ 8, 13 ], [ 16 ], [ 15, 17 ], [ 16, 18 ], 
              [ 17 ], [ 20 ], [ 19 ] ],
          autGroup := Group( [ ( 9,14)(10,13)(11,12), ( 8, 9)(10,14)(11,13), ( 2, 7)( 3, 6)( 4, 5), 
              ( 1, 2)( 3, 7)( 4, 6), ( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14), (19,20), (15,18)(16,17) ] ),
          forms := [ rec(
                  forms := [ [ "[28, 7, 28]" ] ],
                  h := 114 ) ],
          group := Group( [ () ] ),
          h := [ 114 ],
          info := rec(
              bipartite := false,
              distance_regular := false,
              girth := 7,
              pencils := [ [ 2, 16 ], [ 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 := [  ],
          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, 7 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 4, 6 ], [ 5, 7 ], [ 1, 6 ], [ 9, 14 ], 
              [ 8, 10 ], [ 9, 11 ], [ 10, 12 ], [ 11, 13 ], [ 12, 14 ], [ 8, 13 ], [ 16 ], [ 15, 17 ], [ 16 ], 
              [ 19 ], [ 18, 20 ], [ 19 ] ],
          autGroup := Group( [ ( 9,14)(10,13)(11,12), ( 8, 9)(10,14)(11,13), ( 2, 7)( 3, 6)( 4, 5), 
              ( 1, 2)( 3, 7)( 4, 6), ( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14), (18,20), (15,17), 
              (15,18)(16,19)(17,20) ] ),
          forms := [ rec(
                  forms := [ [ "[28, 0, 28]" ] ],
                  h := 116 ) ],
          group := Group( [ () ] ),
          h := [ 116 ],
          info := rec(
              bipartite := false,
              distance_regular := false,
              girth := 7,
              pencils := [ [ 2, 16 ], [ 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 := [  ],
          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, 7 ], [ 1, 3 ], [ 2, 4 ], [ 3, 5 ], [ 4, 6 ], [ 5, 7 ], [ 1, 6 ], [ 9, 14 ], 
              [ 8, 10 ], [ 9, 11 ], [ 10, 12 ], [ 11, 13 ], [ 12, 14 ], [ 8, 13 ], [ 16 ], [ 15 ], [ 18 ], [ 17 ], 
              [  ], [  ] ],
          autGroup := Group( [ ( 9,14)(10,13)(11,12), ( 8, 9)(10,14)(11,13), ( 2, 7)( 3, 6)( 4, 5), 
              ( 1, 2)( 3, 7)( 4, 6), ( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14), (17,18), (15,16), 
              (15,17)(16,18), (19,20) ] ),
          forms := [ rec(
                  forms := [ [ "[42, 0, 42]" ] ],
                  h := 114 ) ],
          group := Group( [ () ] ),
          h := [ 114 ],
          info := rec(
              bipartite := false,
              distance_regular := false,
              girth := 7,
              pencils := [ [ 2, 14 ], [ 1, 4 ], [ 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 := [ 112, 114, 116, 118, 120, 122, 124 ],
  hh := [ rec(
          count := [ 21 ],
          deg := 7,
          h := 112,
          real := [ 21 ] ), rec(
          count := [ 20, 21 ],
          deg := 7,
          h := 114,
          real := [  ] ), rec(
          count := [ 20, 21 ],
          deg := 7,
          h := 116,
          real := [  ] ), rec(
          count := [  ],
          deg := 7,
          h := 118,
          real := [  ] ), rec(
          count := [ 21 ],
          deg := 7,
          h := 120,
          real := [  ] ), rec(
          count := [  ],
          deg := 7,
          h := 122,
          real := [  ] ), rec(
          count := [  ],
          deg := 7,
          h := 124,
          real := [  ] ) ] );

