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On this page are computer-accessible forms for the graph C4[ 168, 59 ] = SDD(PS(6,7;2)).

(I) Following is a form readable by MAGMA:

g:=Graph<168|{ {84, 119}, {82, 118}, {83, 119}, {80, 117}, {81, 118}, {84, 124}, {81, 120}, {82, 123}, {83, 121}, {68, 111}, {66, 110}, {67, 111}, {64, 109}, {80, 126}, {65, 110}, {70, 118}, {76, 124}, {73, 123}, {68, 119}, {78, 125}, {75, 120}, {66, 118}, {77, 121}, {74, 126}, {69, 113}, {64, 117}, {79, 122}, {72, 125}, {69, 112}, {65, 116}, {67, 117}, {71, 113}, {70, 112}, {74, 114}, {75, 115}, {72, 113}, {77, 116}, {78, 116}, {79, 117}, {73, 114}, {71, 122}, {76, 115}, {27, 91}, {37, 101}, {47, 111}, {48, 112}, {26, 91}, {29, 92}, {46, 111}, {24, 90}, {33, 99}, {31, 93}, {30, 92}, {25, 91}, {44, 110}, {50, 112}, {45, 110}, {39, 99}, {25, 92}, {37, 96}, {34, 103}, {38, 96}, {39, 97}, {43, 109}, {28, 91}, {35, 100}, {16, 88}, {43, 99}, {42, 98}, {17, 89}, {32, 105}, {40, 97}, {45, 100}, {19, 89}, {62, 116}, {59, 113}, {46, 100}, {47, 101}, {18, 89}, {41, 98}, {57, 114}, {22, 90}, {63, 115}, {36, 104}, {20, 89}, {42, 103}, {41, 100}, {23, 90}, {58, 119}, {17, 95}, {40, 102}, {21, 90}, {61, 114}, {60, 115}, {38, 105}, {44, 99}, {6, 86}, {59, 107}, {58, 106}, {4, 85}, {61, 108}, {7, 86}, {56, 105}, {62, 108}, {63, 109}, {5, 86}, {13, 94}, {52, 103}, {57, 106}, {1, 85}, {9, 93}, {50, 102}, {51, 103}, {10, 95}, {13, 88}, {48, 101}, {56, 109}, {3, 85}, {14, 88}, {2, 85}, {60, 107}, {15, 88}, {49, 102}, {6, 94}, {5, 92}, {51, 106}, {54, 108}, {12, 87}, {49, 106}, {55, 108}, {1, 93}, {11, 87}, {10, 87}, {53, 104}, {8, 86}, {9, 87}, {53, 107}, {54, 104}, {55, 105}, {52, 107}, {2, 98}, {27, 122}, {24, 122}, {28, 123}, {19, 120}, {20, 121}, {14, 96}, {23, 121}, {16, 126}, {12, 126}, {18, 97}, {22, 98}, {8, 125}, {21, 96}, {11, 125}, {30, 104}, {15, 120}, {3, 123}, {29, 101}, {4, 124}, {31, 102}, {4, 127}, {36, 95}, {26, 97}, {7, 124}, {3, 127}, {35, 95}, {34, 94}, {2, 127}, {32, 93}, {1, 127}, {33, 94}, {5, 134}, {10, 137}, {14, 138}, {5, 128}, {13, 136}, {1, 135}, {6, 128}, {7, 128}, {8, 128}, {9, 129}, {11, 129}, {10, 129}, {14, 130}, {30, 146}, {12, 129}, {15, 130}, {2, 140}, {9, 135}, {6, 136}, {13, 130}, {31, 144}, {19, 131}, {18, 131}, {26, 139}, {21, 132}, {16, 130}, {29, 143}, {22, 132}, {17, 131}, {23, 132}, {20, 131}, {17, 137}, {31, 135}, {30, 134}, {18, 139}, {28, 133}, {22, 140}, {29, 134}, {58, 161}, {24, 132}, {25, 133}, {27, 133}, {21, 138}, {26, 133}, {25, 134}, {46, 142}, {62, 158}, {59, 155}, {47, 143}, {53, 149}, {54, 150}, {7, 166}, {61, 156}, {60, 157}, {44, 141}, {49, 144}, {52, 149}, {55, 150}, {4, 166}, {63, 157}, {50, 144}, {51, 145}, {40, 139}, {45, 142}, {12, 168}, {54, 146}, {55, 147}, {41, 140}, {49, 148}, {52, 145}, {57, 156}, {3, 165}, {42, 140}, {43, 141}, {32, 135}, {41, 142}, {51, 148}, {53, 146}, {50, 154}, {63, 151}, {62, 150}, {33, 136}, {60, 149}, {34, 136}, {39, 141}, {37, 143}, {35, 137}, {48, 154}, {56, 147}, {61, 150}, {11, 167}, {39, 139}, {38, 138}, {33, 141}, {15, 162}, {36, 137}, {35, 142}, {57, 148}, {58, 148}, {59, 149}, {8, 167}, {37, 138}, {56, 151}, {19, 162}, {32, 147}, {34, 145}, {23, 163}, {44, 152}, {38, 147}, {45, 152}, {36, 146}, {47, 153}, {20, 163}, {46, 153}, {16, 168}, {40, 144}, {28, 165}, {42, 145}, {24, 164}, {43, 151}, {27, 164}, {48, 143}, {80, 159}, {78, 158}, {79, 159}, {76, 157}, {72, 155}, {77, 158}, {73, 156}, {74, 156}, {75, 157}, {64, 151}, {65, 152}, {66, 152}, {67, 153}, {67, 159}, {71, 155}, {70, 154}, {68, 153}, {69, 155}, {64, 159}, {69, 154}, {65, 158}, {66, 160}, {74, 168}, {71, 164}, {68, 161}, {70, 160}, {75, 162}, {78, 167}, {76, 166}, {79, 164}, {73, 165}, {77, 163}, {72, 167}, {83, 163}, {81, 160}, {82, 160}, {84, 166}, {83, 161}, {81, 162}, {84, 161}, {82, 165}, {80, 168} }>;

(II) A more general form is to represent the graph as the orbit of {84, 119} under the group generated by the following permutations:

a: (97, 139)
b: (91, 133)
c: (87, 129)
d: (113, 155)
e: (101, 143)
f: (109, 151)
g: (120, 162)
h: (117, 159)
m: (108, 150)
n1: (110, 152)
a1: (103, 145)
b1: (98, 140)
c1: (112, 154)
d1: (111, 153)
e1: (1, 2)(3, 4)(5, 25)(6, 26)(7, 28)(8, 27)(9, 22)(10, 21)(11, 24)(12, 23)(13, 18)(14, 17)(15, 19)(16, 20)(29, 30)(31, 42)(32, 41)(33, 39)(34, 40)(35, 38)(36, 37)(43, 44)(45, 56)(46, 55)(47, 54)(48, 53)(49, 51)(50, 52)(57, 58)(59, 69)(60, 70)(61, 68)(62, 67)(63, 66)(64, 65)(71, 72)(73, 84)(74, 83)(75, 81)(76, 82)(77, 80)(78, 79)(86, 91)(87, 90)(88, 89)(93, 98)(94, 97)(95, 96)(100, 105)(101, 104)(102, 103)(107, 112)(108, 111)(109, 110)(114, 119)(115, 118)(116, 117)(121, 126)(122, 125)(123, 124)(128, 133)(129, 132)(130, 131)(135, 140)(136, 139)(137, 138)(142, 147)(143, 146)(144, 145)(149, 154)(150, 153)(151, 152)(156, 161)(157, 160)(158, 159)(163, 168)(164, 167)(165, 166)
f1: (106, 148)
g1: (104, 146)
h1: (124, 166)
m1: (126, 168)
n2: (115, 157)
a2: (96, 138)
b2: (86, 128)
c2: (90, 132)
d2: (121, 163)
e2: (122, 164)
f2: (123, 165)
g2: (102, 144)
h2: (92, 134)
m2: (119, 161)
n3: (107, 149)
a3: (5, 75)(6, 60)(7, 76)(8, 63)(9, 32)(10, 38)(11, 56)(12, 55)(13, 53)(14, 36)(15, 30)(16, 54)(17, 37)(18, 48)(19, 29)(20, 47)(21, 35)(22, 41)(23, 46)(24, 45)(25, 81)(26, 70)(27, 66)(28, 82)(33, 59)(34, 52)(39, 69)(40, 50)(43, 72)(44, 71)(61, 74)(62, 80)(64, 78)(65, 79)(67, 77)(68, 83)(86, 115)(87, 105)(88, 104)(89, 101)(90, 100)(91, 118)(92, 120)(94, 107)(95, 96)(97, 112)(99, 113)(108, 126)(109, 125)(110, 122)(111, 121)(116, 117)(128, 157)(129, 147)(130, 146)(131, 143)(132, 142)(133, 160)(134, 162)(136, 149)(137, 138)(139, 154)(141, 155)(150, 168)(151, 167)(152, 164)(153, 163)(158, 159)
b3: (118, 160)
c3: (85, 127)
d3: (2, 9)(3, 31)(4, 32)(5, 37)(6, 14)(7, 38)(8, 21)(10, 41)(11, 22)(12, 42)(15, 33)(16, 34)(17, 45)(18, 66)(19, 44)(20, 65)(23, 78)(24, 72)(25, 48)(26, 70)(27, 69)(28, 50)(30, 47)(36, 46)(39, 81)(40, 82)(43, 75)(49, 73)(51, 74)(52, 80)(53, 67)(54, 68)(55, 84)(56, 76)(58, 61)(59, 79)(60, 64)(62, 83)(85, 93)(86, 96)(87, 98)(88, 94)(89, 110)(90, 125)(91, 112)(92, 101)(95, 100)(97, 118)(99, 120)(102, 123)(103, 126)(104, 111)(105, 124)(106, 114)(107, 117)(108, 119)(109, 115)(113, 122)(116, 121)(127, 135)(128, 138)(129, 140)(130, 136)(131, 152)(132, 167)(133, 154)(134, 143)(137, 142)(139, 160)(141, 162)(144, 165)(145, 168)(146, 153)(147, 166)(148, 156)(149, 159)(150, 161)(151, 157)(155, 164)(158, 163)
e3: (125, 167)
f3: (100, 142)
g3: (94, 136)
h3: (116, 158)
m3: (99, 141)
n4: (89, 131)
a4: (114, 156)
b4: (105, 147)
c4: (93, 135)
d4: (95, 137)

(III) Last is Groups&Graphs. Copy everything between (not including) the lines of asterisks into a plain text file and save it as "graph.txt". Then launch G&G (Groups&Graphs) and select Read Text from the File menu.

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&Graph
C4[ 168, 59 ]
168
-1 135 93 127 85
-2 127 85 140 98
-3 165 123 127 85
-4 166 124 127 85
-5 134 92 128 86
-6 136 94 128 86
-7 166 124 128 86
-8 167 125 128 86
-9 135 93 129 87
-10 137 95 129 87
-11 167 125 129 87
-12 168 126 129 87
-13 88 136 94 130
-14 88 138 96 130
-15 88 162 130 120
-16 88 168 126 130
-17 89 137 95 131
-18 89 139 97 131
-19 89 162 120 131
-20 121 89 163 131
-21 132 90 138 96
-22 132 90 140 98
-23 121 132 90 163
-24 132 122 90 164
-25 133 134 91 92
-26 133 91 139 97
-27 122 133 91 164
-28 165 133 123 91
-29 143 101 134 92
-30 134 146 92 104
-31 144 102 135 93
-32 135 147 93 105
-33 99 136 94 141
-34 145 103 136 94
-35 100 137 95 142
-36 146 104 137 95
-37 143 101 138 96
-38 147 105 138 96
-39 99 139 97 141
-40 144 102 139 97
-41 100 140 98 142
-42 145 103 140 98
-43 99 151 141 109
-44 99 110 141 152
-45 110 100 152 142
-46 100 111 142 153
-47 143 111 101 153
-48 143 154 101 112
-49 144 102 148 106
-50 154 144 112 102
-51 145 103 148 106
-52 145 103 149 107
-53 146 104 149 107
-54 146 104 150 108
-55 147 105 150 108
-56 147 105 151 109
-57 156 114 148 106
-58 148 106 161 119
-59 155 113 149 107
-60 157 115 149 107
-61 156 114 150 108
-62 158 116 150 108
-63 157 115 151 109
-64 159 117 151 109
-65 110 158 116 152
-66 110 160 118 152
-67 111 159 117 153
-68 111 161 119 153
-69 154 155 112 113
-70 154 112 160 118
-71 122 155 113 164
-72 155 167 113 125
-73 165 123 156 114
-74 156 168 114 126
-75 157 115 162 120
-76 166 124 157 115
-77 121 158 116 163
-78 167 125 158 116
-79 122 159 117 164
-80 168 126 159 117
-81 160 118 162 120
-82 165 123 160 118
-83 121 161 119 163
-84 166 124 161 119
-85 1 2 3 4
-86 5 6 7 8
-87 11 12 9 10
-88 13 14 15 16
-89 17 18 19 20
-90 22 23 24 21
-91 25 26 27 28
-92 25 5 29 30
-93 1 9 31 32
-94 33 34 13 6
-95 35 36 17 10
-96 14 37 38 21
-97 26 39 18 40
-98 22 2 41 42
-99 33 44 39 43
-100 45 35 46 41
-101 47 37 48 29
-102 49 50 40 31
-103 34 51 52 42
-104 36 30 53 54
-105 55 56 38 32
-106 57 58 49 51
-107 59 60 52 53
-108 55 61 62 54
-109 56 63 64 43
-110 44 66 45 65
-111 67 46 68 47
-112 69 48 70 50
-113 69 59 71 72
-114 57 61 73 74
-115 60 63 75 76
-116 77 78 62 65
-117 67 79 80 64
-118 66 70 81 82
-119 68 58 83 84
-120 15 81 19 75
-121 77 23 83 20
-122 24 79 27 71
-123 3 82 28 73
-124 4 7 84 76
-125 11 78 72 8
-126 12 80 16 74
-127 1 2 3 4
-128 5 6 7 8
-129 11 12 9 10
-130 13 14 15 16
-131 17 18 19 20
-132 22 23 24 21
-133 25 26 27 28
-134 25 5 29 30
-135 1 9 31 32
-136 33 34 13 6
-137 35 36 17 10
-138 14 37 38 21
-139 26 39 18 40
-140 22 2 41 42
-141 33 44 39 43
-142 45 35 46 41
-143 47 37 48 29
-144 49 50 40 31
-145 34 51 52 42
-146 36 30 53 54
-147 55 56 38 32
-148 57 58 49 51
-149 59 60 52 53
-150 55 61 62 54
-151 56 63 64 43
-152 44 66 45 65
-153 67 46 68 47
-154 69 48 70 50
-155 69 59 71 72
-156 57 61 73 74
-157 60 63 75 76
-158 77 78 62 65
-159 67 79 80 64
-160 66 70 81 82
-161 68 58 83 84
-162 15 81 19 75
-163 77 23 83 20
-164 24 79 27 71
-165 3 82 28 73
-166 4 7 84 76
-167 11 78 72 8
-168 12 80 16 74
0

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