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On this page are computer-accessible forms for the graph C4[ 168, 53 ] = HC(F28).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {100, 101} under the group generated by the following permutations:

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

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

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