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On this page are computer-accessible forms for the graph C4[ 168, 65 ] = BGCG(L(F56C);K1;{6,9}).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {68, 93} under the group generated by the following permutations:

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

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

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