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On this page are computer-accessible forms for the graph C4[ 168, 9 ] = PS(24,7;2).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {28, 29} under the group generated by the following permutations:

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

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

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