# -*- GAP -*-

e6p_pencil :=
rec(
  graph := [ rec(
          adjacencies := [ [ 2 ], [ 1, 3 ], [ 2, 4, 6 ], [ 3, 5 ], [ 4 ], [ 3, 7 ], [ 6 ], [ 9 ], [ 8, 10 ], 
              [ 9, 11, 13 ], [ 10, 12 ], [ 11 ], [ 10, 14 ], [ 13 ], [ 16 ], [ 15, 17 ], [ 16, 18, 20 ], [ 17, 19 ], 
              [ 18 ], [ 17, 21 ], [ 20 ] ],
          autGroup := Group( [ ( 4, 6)( 5, 7), (11,13)(12,14), (18,20)(19,21), (15,19)(16,18), ( 8,12)( 9,11), 
              ( 8,15)( 9,16)(10,17)(11,18)(12,19)(13,20)(14,21), ( 1, 5)( 2, 4), ( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)
                ( 6,13)( 7,14) ] ),
          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 := -1,
              pencils := [ [ 3, 3 ], [ 2, 9 ], [ 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, 21 ],
          order := 21,
          real := [ 318, 324 ],
          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 ], [ 1, 3 ], [ 2, 4, 6 ], [ 3, 5 ], [ 4 ], [ 3, 7 ], [ 6 ], [ 9 ], [ 8, 10 ], 
              [ 9, 11, 13 ], [ 10, 12 ], [ 11 ], [ 10, 14 ], [ 13 ], [ 20 ], [ 20 ], [ 18 ], [ 17, 19 ], [ 18, 20 ], 
              [ 15, 16, 19 ] ],
          autGroup := Group( [ ( 4, 6)( 5, 7), (11,13)(12,14), ( 8,12)( 9,11), ( 1, 5)( 2, 4), 
              ( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14), (15,16) ] ),
          forms := [ rec(
                  forms := [ [ "[12, 0, 48]" ] ],
                  h := 320 ), rec(
                  forms := [ [ "[12, 0, 48]" ] ],
                  h := 332 ) ],
          group := Group( [ () ] ),
          h := [ 320, 332 ],
          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, 6 ], [ 3, 5 ], [ 4 ], [ 3, 7 ], [ 6 ], [ 9 ], [ 8, 10 ], 
              [ 9, 11, 13 ], [ 10, 12 ], [ 11 ], [ 10, 14 ], [ 13 ], [ 18 ], [ 18 ], [ 18 ], [ 15, 16, 17 ], [  ], 
              [  ] ],
          autGroup := Group( [ ( 4, 6)( 5, 7), (11,13)(12,14), ( 8,12)( 9,11), ( 1, 5)( 2, 4), 
              ( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14), (16,17), (15,16), (19,20) ] ),
          forms := [ rec(
                  forms := [ [ "[12, 0, 48]" ] ],
                  h := 312 ), rec(
                  forms := [ [ "[12, 0, 48]" ] ],
                  h := 324 ) ],
          group := Group( [ () ] ),
          h := [ 312, 324 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := -1,
              pencils := [ [ 3, 3 ], [ 2, 6 ], [ 1, 9 ], [ 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 ] ), rec(
          adjacencies := [ [ 2 ], [ 1, 3 ], [ 2, 4, 6 ], [ 3, 5 ], [ 4 ], [ 3, 7 ], [ 6 ], [ 9 ], [ 8, 10 ], 
              [ 9, 11, 13 ], [ 10, 12 ], [ 11 ], [ 10, 14 ], [ 13 ], [ 16 ], [ 15, 17 ], [ 16, 18 ], [ 17, 19 ], 
              [ 18, 20 ], [ 19 ] ],
          autGroup := Group( [ (15,20)(16,19)(17,18), ( 4, 6)( 5, 7), (11,13)(12,14), ( 8,12)( 9,11), ( 1, 5)( 2, 4), 
              ( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14) ] ),
          forms := [ rec(
                  forms := [ [ "[6, 0, 168]" ] ],
                  h := 314 ), rec(
                  forms := [ [ "[12, 6, 24]" ], [ "[24, 12, 48]" ], [ "[6, 0, 42]" ], [ "[6, 3, 12]" ] ],
                  h := 320 ), rec(
                  forms := [ [ "[24, 0, 42]" ] ],
                  h := 326 ), rec(
                  forms := [ [ "[12, 0, 84]" ] ],
                  h := 332 ) ],
          group := Group( [ () ] ),
          h := [ 314, 320, 326, 332 ],
          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, 6 ], [ 3, 5 ], [ 4 ], [ 3, 7 ], [ 6 ], [ 9 ], [ 8, 10 ], 
              [ 9, 11, 13 ], [ 10, 12 ], [ 11 ], [ 10, 14 ], [ 13 ], [ 16 ], [ 15, 17 ], [ 16, 18 ], [ 17, 19 ], 
              [ 18 ], [  ] ],
          autGroup := Group( [ (15,19)(16,18), ( 4, 6)( 5, 7), (11,13)(12,14), ( 8,12)( 9,11), ( 1, 5)( 2, 4), 
              ( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14) ] ),
          forms := [ rec(
                  forms := [ [ "[8, 0, 24]" ] ],
                  h := 312 ), rec(
                  forms := [ [ "[24, 0, 72]" ] ],
                  h := 320 ), rec(
                  forms := [ [ "[8, 0, 24]" ] ],
                  h := 324 ), rec(
                  forms := [ [ "[24, 0, 72]" ] ],
                  h := 332 ) ],
          group := Group( [ () ] ),
          h := [ 312, 320, 324, 332 ],
          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, 6 ], [ 3, 5 ], [ 4 ], [ 3, 7 ], [ 6 ], [ 9 ], [ 8, 10 ], 
              [ 9, 11, 13 ], [ 10, 12 ], [ 11 ], [ 10, 14 ], [ 13 ], [ 16 ], [ 15, 17 ], [ 16 ], [ 19 ], [ 18, 20 ], 
              [ 19 ] ],
          autGroup := Group( [ (18,20), (15,17), (15,18)(16,19)(17,20), ( 4, 6)( 5, 7), (11,13)(12,14), 
              ( 8,12)( 9,11), ( 1, 5)( 2, 4), ( 1, 8)( 2, 9)( 3,10)( 4,11)( 5,12)( 6,13)( 7,14) ] ),
          forms := [ rec(
                  forms := [ [ "[6, 0, 6]" ] ],
                  h := 314 ), rec(
                  forms := [ [ "[24, 0, 24]" ], [ "[6, 0, 24]" ] ],
                  h := 320 ), rec(
                  forms := [ [ "[12, 0, 12]" ] ],
                  h := 326 ) ],
          group := Group( [ () ] ),
          h := [ 314, 320, 326 ],
          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, 6 ], [ 3, 5 ], [ 4 ], [ 3, 7 ], [ 6 ], [ 15 ], [ 15 ], [ 12 ], 
              [ 12 ], [ 10, 11, 13 ], [ 12, 14 ], [ 13, 15 ], [ 8, 9, 14 ], [ 20 ], [ 20 ], [ 19 ], [ 18, 20 ], 
              [ 16, 17, 19 ] ],
          autGroup := Group( [ ( 4, 6)( 5, 7), ( 1, 5)( 2, 4), (10,11), ( 8, 9), ( 8,10)( 9,11)(12,15)(13,14), 
              (16,17) ] ),
          forms := [ rec(
                  forms := [ [ "[36, 0, 48]" ] ],
                  h := 312 ), rec(
                  forms := [ [ "[4, 0, 48]" ] ],
                  h := 320 ), rec(
                  forms := [ [ "[36, 0, 48]" ] ],
                  h := 324 ), rec(
                  forms := [ [ "[4, 0, 48]" ] ],
                  h := 332 ) ],
          group := Group( [ () ] ),
          h := [ 312, 320, 324, 332 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := -1,
              pencils := [ [ 3, 4 ], [ 2, 6 ], [ 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, 6 ], [ 3, 5 ], [ 4 ], [ 3, 7 ], [ 6 ], [ 15 ], [ 15 ], [ 12 ], 
              [ 12 ], [ 10, 11, 13 ], [ 12, 14 ], [ 13, 15 ], [ 8, 9, 14 ], [ 17 ], [ 16, 18 ], [ 17, 19 ], [ 18 ], 
              [  ] ],
          autGroup := Group( [ ( 4, 6)( 5, 7), ( 1, 5)( 2, 4), (16,19)(17,18), (10,11), ( 8, 9), 
              ( 8,10)( 9,11)(12,15)(13,14) ] ),
          forms := [ rec(
                  forms := [ [ "[36, 0, 480]" ] ],
                  h := 312 ), rec(
                  forms := [ [ "[4, 0, 480]" ] ],
                  h := 320 ), rec(
                  forms := [ [ "[36, 0, 480]" ] ],
                  h := 324 ), rec(
                  forms := [ [ "[4, 0, 480]" ] ],
                  h := 332 ) ],
          group := Group( [ () ] ),
          h := [ 312, 320, 324, 332 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := -1,
              pencils := [ [ 3, 3 ], [ 2, 7 ], [ 1, 9 ], [ 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, 6 ], [ 3, 5 ], [ 4 ], [ 3, 7 ], [ 6 ], [ 15 ], [ 15 ], [ 12 ], 
              [ 12 ], [ 10, 11, 13 ], [ 12, 14 ], [ 13, 15 ], [ 8, 9, 14 ], [ 17 ], [ 16, 18 ], [ 17 ], [  ], [  ] ],
          autGroup := Group( [ ( 4, 6)( 5, 7), ( 1, 5)( 2, 4), (16,18), (10,11), ( 8, 9), 
              ( 8,10)( 9,11)(12,15)(13,14), (19,20) ] ),
          forms := [ rec(
                  forms := [ [ "[36, 0, 48]" ] ],
                  h := 312 ), rec(
                  forms := [ [ "[4, 0, 48]" ] ],
                  h := 320 ), rec(
                  forms := [ [ "[36, 0, 48]" ] ],
                  h := 324 ), rec(
                  forms := [ [ "[4, 0, 48]" ] ],
                  h := 332 ) ],
          group := Group( [ () ] ),
          h := [ 312, 320, 324, 332 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := -1,
              pencils := [ [ 3, 3 ], [ 2, 6 ], [ 1, 9 ], [ 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 ] ), rec(
          adjacencies := [ [ 2 ], [ 1, 3 ], [ 2, 4, 6 ], [ 3, 5 ], [ 4 ], [ 3, 7 ], [ 6 ], [ 9, 19 ], [ 8, 10 ], 
              [ 9, 11 ], [ 10, 12 ], [ 11, 13 ], [ 12, 14 ], [ 13, 15 ], [ 14, 16 ], [ 15, 17 ], [ 16, 18 ], 
              [ 17, 19 ], [ 8, 18 ], [  ] ],
          autGroup := Group( [ ( 9,19)(10,18)(11,17)(12,16)(13,15), ( 8, 9)(10,19)(11,18)(12,17)(13,16)(14,15), 
              ( 4, 6)( 5, 7), ( 1, 5)( 2, 4) ] ),
          forms := [ rec(
                  forms := [ [ "[32, 16, 44]" ] ],
                  h := 312 ), rec(
                  forms := [ [ "[16, 8, 76]" ] ],
                  h := 316 ), rec(
                  forms := [ [ "[12, 0, 96]" ], [ "[12, 4, 12]" ] ],
                  h := 320 ), rec(
                  forms := [ [ "[32, 16, 44]" ] ],
                  h := 324 ), rec(
                  forms := [ [ "[16, 8, 76]" ] ],
                  h := 328 ), rec(
                  forms := [ [ "[12, 0, 96]" ], [ "[12, 4, 12]" ] ],
                  h := 332 ) ],
          group := Group( [ () ] ),
          h := [ 312, 316, 320, 324, 328, 332 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := 12,
              pencils := [ [ 3, 1 ], [ 2, 15 ], [ 1, 3 ], [ 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 := [ 312, 314, 316, 318, 320, 322, 324, 326, 328, 330, 332, 334 ],
  hh := [ rec(
          count := [ 20, 21 ],
          deg := 12,
          h := 312,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 12,
          h := 314,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 12,
          h := 316,
          real := [  ] ), rec(
          count := [ 21 ],
          deg := 12,
          h := 318,
          real := [ 21 ] ), rec(
          count := [ 20, 21 ],
          deg := 12,
          h := 320,
          real := [  ] ), rec(
          count := [  ],
          deg := 12,
          h := 322,
          real := [  ] ), rec(
          count := [ 20, 21 ],
          deg := 12,
          h := 324,
          real := [ 21 ] ), rec(
          count := [ 20, 21 ],
          deg := 12,
          h := 326,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 12,
          h := 328,
          real := [  ] ), rec(
          count := [  ],
          deg := 12,
          h := 330,
          real := [  ] ), rec(
          count := [ 20, 21 ],
          deg := 12,
          h := 332,
          real := [  ] ), rec(
          count := [  ],
          deg := 12,
          h := 334,
          real := [  ] ) ] );

