# -*- GAP -*-

d5p_pencil :=
rec(
  graph := [ rec(
          adjacencies := [ [ 6 ], [ 6 ], [ 5 ], [ 5 ], [ 3, 4, 6 ], [ 1, 2, 5 ], [ 12 ], [ 12 ], [ 11 ], [ 11 ], 
              [ 9, 10, 12 ], [ 7, 8, 11 ], [ 14, 20 ], [ 13, 15 ], [ 14, 16 ], [ 15, 17 ], [ 16, 18 ], [ 17, 19 ], 
              [ 18, 20 ], [ 13, 19 ], [  ] ],
          autGroup := Group( [ (14,20)(15,19)(16,18), (13,14)(15,20)(16,19)(17,18), ( 9,10), ( 7, 8), 
              ( 7, 9)( 8,10)(11,12), ( 3, 4), ( 1, 2), ( 1, 3)( 2, 4)( 5, 6), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)
                ( 6,12) ] ),
          forms := [ rec(
                  forms := [ [ "[32, 16, 40]" ] ],
                  h := 144 ), rec(
                  forms := [ [ "[32, 16, 40]" ] ],
                  h := 148 ), rec(
                  forms := [ [ "[32, 16, 40]" ] ],
                  h := 152 ), rec(
                  forms := [ [ "[32, 16, 40]" ] ],
                  h := 156 ) ],
          group := Group( [ () ] ),
          h := [ 144, 148, 152, 156 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := 8,
              pencils := [ [ 3, 4 ], [ 2, 8 ], [ 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, 21 ],
          order := 21,
          real := [  ],
          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 := [ [ 6 ], [ 6 ], [ 5 ], [ 5 ], [ 3, 4, 6 ], [ 1, 2, 5 ], [ 12 ], [ 12 ], [ 11 ], [ 11 ], 
              [ 9, 10, 12 ], [ 7, 8, 11 ], [ 18 ], [ 18 ], [ 17 ], [ 17 ], [ 15, 16, 18 ], [ 13, 14, 17 ], [ 20 ], 
              [ 19 ] ],
          autGroup := Group( [ (15,16), (13,14), (13,15)(14,16)(17,18), ( 9,10), ( 7, 8), ( 7, 9)( 8,10)(11,12), 
              ( 7,13)( 8,14)( 9,15)(10,16)(11,17)(12,18), ( 3, 4), ( 1, 2), ( 1, 3)( 2, 4)( 5, 6), 
              ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12), (19,20) ] ),
          forms := [ rec(
                  forms := [ [ "[-16] + [8, 4, 8]" ] ],
                  h := 144 ), rec(
                  forms := [ [ "[-12] + [4] + [4]", "[-4] + [8, 4, 8]" ] ],
                  h := 148 ), rec(
                  forms := [ [ "[-48] + [4] + [4]", "[-12] + [4] + [16]" ] ],
                  h := 152 ), rec(
                  forms := [ [ "[-12] + [8] + [8]", "[-8] + [4] + [24]", "[-4] + [8] + [24]" ] ],
                  h := 156 ) ],
          group := Group( [ () ] ),
          h := [ 144, 148, 152, 156 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := -1,
              pencils := [ [ 3, 6 ], [ 1, 14 ] ],
              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 := [ [ 6 ], [ 6 ], [ 5 ], [ 5 ], [ 3, 4, 6 ], [ 1, 2, 5 ], [ 12 ], [ 12 ], [ 11 ], [ 11 ], 
              [ 9, 10, 12 ], [ 7, 8, 11 ], [ 14, 20 ], [ 13, 15 ], [ 14, 16 ], [ 15, 17 ], [ 16, 18 ], [ 17, 19 ], 
              [ 18, 20 ], [ 13, 19 ] ],
          autGroup := Group( [ (14,20)(15,19)(16,18), (13,14)(15,20)(16,19)(17,18), ( 9,10), ( 7, 8), 
              ( 7, 9)( 8,10)(11,12), ( 3, 4), ( 1, 2), ( 1, 3)( 2, 4)( 5, 6), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)
                ( 6,12) ] ),
          forms := [ rec(
                  forms := [ [ "[-4] + [12, 4, 12]" ] ],
                  h := 144 ), rec(
                  forms := [ [  ] ],
                  h := 146 ), rec(
                  forms := [ [  ], [ "[-2] + [8, 4, 10]" ] ],
                  h := 148 ), rec(
                  forms := [ [ "[-16] + [6, 2, 6]" ] ],
                  h := 150 ), rec(
                  forms := [ [ "[-32] + [4] + [4]" ] ],
                  h := 152 ), rec(
                  forms := [ [ "U(16) + [2]" ] ],
                  h := 154 ), rec(
                  forms := [ [ "U(1) + [32]" ], [ "U(2) + [32]" ], [ "U(4) + [32]" ], [ "[-4] + [4] + [32]" ] ],
                  h := 156 ), rec(
                  forms := [ [ "[-2] + [16] + [16]" ] ],
                  h := 158 ) ],
          group := Group( [ () ] ),
          h := [ 144, 146, 148, 150, 152, 154, 156, 158 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := 8,
              pencils := [ [ 3, 4 ], [ 2, 8 ], [ 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 := [ 148, 154, 156 ],
          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 := [ [ 6 ], [ 6 ], [ 5 ], [ 5 ], [ 3, 4, 6 ], [ 1, 2, 5 ], [ 12 ], [ 12 ], [ 11 ], [ 11 ], 
              [ 9, 10, 12 ], [ 7, 8, 11 ], [ 14 ], [ 13, 15 ], [ 14, 16 ], [ 15 ], [ 18 ], [ 17, 19 ], [ 18, 20 ], 
              [ 19 ] ],
          autGroup := Group( [ (17,20)(18,19), (13,16)(14,15), (13,17)(14,18)(15,19)(16,20), ( 9,10), ( 7, 8), 
              ( 7, 9)( 8,10)(11,12), ( 3, 4), ( 1, 2), ( 1, 3)( 2, 4)( 5, 6), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)
                ( 6,12) ] ),
          forms := [ rec(
                  forms := [ [ "[20, 0, 20]" ] ],
                  h := 144 ), rec(
                  forms := [ [ "[20, 0, 80]" ] ],
                  h := 148 ), rec(
                  forms := [ [ "[40, 0, 40]" ] ],
                  h := 152 ) ],
          group := Group( [ () ] ),
          h := [ 144, 148, 152 ],
          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 := [ [ 6 ], [ 6 ], [ 5 ], [ 5 ], [ 3, 4, 6 ], [ 1, 2, 5 ], [ 8, 14 ], [ 7, 9 ], [ 8, 10 ], 
              [ 9, 11 ], [ 10, 12 ], [ 11, 13 ], [ 12, 14 ], [ 7, 13 ], [ 16 ], [ 15, 17 ], [ 16, 18 ], [ 17 ], [  ], 
              [  ] ],
          autGroup := Group( [ ( 8,14)( 9,13)(10,12), ( 7, 8)( 9,14)(10,13)(11,12), (15,18)(16,17), ( 3, 4), ( 1, 2), 
              ( 1, 3)( 2, 4)( 5, 6), (19,20) ] ),
          forms := [ rec(
                  forms := [ [ "[32, 16, 88]" ] ],
                  h := 148 ), rec(
                  forms := [ [ "[32, 16, 88]" ] ],
                  h := 156 ) ],
          group := Group( [ () ] ),
          h := [ 148, 156 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := 8,
              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 ] ), rec(
          adjacencies := [ [ 6 ], [ 6 ], [ 5 ], [ 5 ], [ 3, 4, 6 ], [ 1, 2, 5 ], [ 8, 14 ], [ 7, 9 ], [ 8, 10 ], 
              [ 9, 11 ], [ 10, 12 ], [ 11, 13 ], [ 12, 14 ], [ 7, 13 ], [ 16 ], [ 15, 17 ], [ 16 ], [ 19 ], [ 18 ], 
              [  ] ],
          autGroup := Group( [ ( 8,14)( 9,13)(10,12), ( 7, 8)( 9,14)(10,13)(11,12), (18,19), ( 3, 4), ( 1, 2), 
              ( 1, 3)( 2, 4)( 5, 6), (15,17) ] ),
          forms := [ rec(
                  forms := [ [ "[32, 16, 104]" ] ],
                  h := 144 ), rec(
                  forms := [ [ "[32, 16, 104]" ] ],
                  h := 148 ), rec(
                  forms := [ [ "[32, 16, 104]" ] ],
                  h := 152 ), rec(
                  forms := [ [ "[32, 16, 104]" ] ],
                  h := 156 ) ],
          group := Group( [ () ] ),
          h := [ 144, 148, 152, 156 ],
          info := rec(
              bipartite := true,
              distance_regular := false,
              girth := 8,
              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 ] ) ],
  h := [ 144, 146, 148, 150, 152, 154, 156, 158 ],
  hh := [ rec(
          count := [ 20, 21 ],
          deg := 8,
          h := 144,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 8,
          h := 146,
          real := [  ] ), rec(
          count := [ 20, 21 ],
          deg := 8,
          h := 148,
          real := [ 20 ] ), rec(
          count := [ 20 ],
          deg := 8,
          h := 150,
          real := [  ] ), rec(
          count := [ 20, 21 ],
          deg := 8,
          h := 152,
          real := [  ] ), rec(
          count := [ 20 ],
          deg := 8,
          h := 154,
          real := [ 20 ] ), rec(
          count := [ 20, 21 ],
          deg := 8,
          h := 156,
          real := [ 20 ] ), rec(
          count := [ 20 ],
          deg := 8,
          h := 158,
          real := [  ] ) ] );

