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On this page are computer-accessible forms for the graph C4[ 171, 7 ] = PS(3,57;7).

(I) Following is a form readable by MAGMA:

g:=Graph<171|{ {57, 58}, {112, 119}, {113, 120}, {114, 121}, {109, 116}, {111, 118}, {110, 117}, {108, 115}, {65, 115}, {68, 118}, {69, 119}, {72, 122}, {73, 123}, {76, 126}, {77, 127}, {66, 116}, {67, 117}, {74, 124}, {75, 125}, {2, 58}, {3, 59}, {4, 60}, {5, 61}, {6, 62}, {7, 63}, {1, 59}, {4, 62}, {5, 63}, {2, 60}, {3, 61}, {70, 120}, {71, 121}, {58, 122}, {59, 123}, {60, 124}, {61, 125}, {62, 126}, {63, 127}, {50, 115}, {52, 117}, {54, 119}, {56, 121}, {53, 118}, {57, 122}, {6, 64}, {39, 97}, {38, 96}, {31, 89}, {30, 88}, {7, 65}, {14, 72}, {15, 73}, {22, 80}, {23, 81}, {46, 104}, {47, 105}, {54, 112}, {55, 113}, {51, 116}, {8, 64}, {41, 97}, {40, 96}, {31, 87}, {30, 86}, {29, 85}, {28, 84}, {27, 83}, {9, 65}, {10, 66}, {11, 67}, {12, 68}, {13, 69}, {14, 70}, {15, 71}, {24, 80}, {25, 81}, {26, 82}, {42, 98}, {43, 99}, {44, 100}, {45, 101}, {46, 102}, {47, 103}, {56, 112}, {57, 113}, {8, 66}, {41, 99}, {40, 98}, {29, 87}, {28, 86}, {9, 67}, {12, 70}, {13, 71}, {24, 82}, {25, 83}, {44, 102}, {45, 103}, {56, 114}, {10, 68}, {27, 85}, {26, 84}, {11, 69}, {42, 100}, {43, 101}, {55, 120}, {16, 72}, {17, 73}, {18, 74}, {19, 75}, {20, 76}, {21, 77}, {22, 78}, {23, 79}, {48, 104}, {49, 105}, {50, 106}, {51, 107}, {52, 108}, {53, 109}, {54, 110}, {55, 111}, {16, 74}, {17, 75}, {20, 78}, {21, 79}, {48, 106}, {49, 107}, {52, 110}, {53, 111}, {18, 76}, {19, 77}, {50, 108}, {51, 109}, {16, 122}, {17, 123}, {20, 126}, {21, 127}, {18, 124}, {19, 125}, {1, 114}, {14, 120}, {15, 121}, {32, 88}, {39, 95}, {38, 94}, {37, 93}, {36, 92}, {35, 91}, {34, 90}, {33, 89}, {1, 123}, {37, 95}, {36, 94}, {33, 91}, {32, 90}, {4, 126}, {5, 127}, {9, 115}, {12, 118}, {13, 119}, {2, 124}, {35, 93}, {34, 92}, {3, 125}, {10, 116}, {11, 117}, {6, 128}, {39, 161}, {38, 160}, {31, 153}, {30, 152}, {7, 129}, {14, 136}, {15, 137}, {22, 144}, {23, 145}, {46, 168}, {47, 169}, {8, 130}, {40, 162}, {29, 151}, {28, 150}, {9, 131}, {12, 134}, {13, 135}, {24, 146}, {25, 147}, {41, 163}, {44, 166}, {45, 167}, {10, 132}, {27, 149}, {26, 148}, {11, 133}, {42, 164}, {43, 165}, {61, 168}, {63, 170}, {22, 128}, {31, 137}, {30, 136}, {23, 129}, {54, 160}, {55, 161}, {62, 169}, {16, 138}, {29, 135}, {28, 134}, {17, 139}, {20, 142}, {21, 143}, {24, 130}, {25, 131}, {48, 170}, {49, 171}, {56, 162}, {57, 163}, {60, 167}, {59, 166}, {18, 140}, {27, 133}, {26, 132}, {19, 141}, {58, 165}, {4, 167}, {8, 171}, {1, 164}, {3, 166}, {2, 165}, {32, 138}, {37, 143}, {36, 142}, {33, 139}, {48, 154}, {49, 155}, {52, 158}, {53, 159}, {5, 168}, {7, 170}, {34, 140}, {35, 141}, {50, 156}, {51, 157}, {6, 169}, {38, 144}, {39, 145}, {46, 152}, {47, 153}, {32, 154}, {41, 147}, {40, 146}, {37, 159}, {36, 158}, {33, 155}, {44, 150}, {45, 151}, {34, 156}, {35, 157}, {42, 148}, {43, 149}, {64, 128}, {107, 171}, {106, 170}, {105, 169}, {104, 168}, {103, 167}, {102, 166}, {101, 165}, {100, 164}, {99, 163}, {98, 162}, {97, 161}, {96, 160}, {95, 159}, {94, 158}, {93, 157}, {92, 156}, {91, 155}, {90, 154}, {89, 153}, {88, 152}, {87, 151}, {86, 150}, {85, 149}, {84, 148}, {65, 129}, {66, 130}, {67, 131}, {68, 132}, {69, 133}, {70, 134}, {71, 135}, {72, 136}, {73, 137}, {74, 138}, {75, 139}, {76, 140}, {77, 141}, {78, 142}, {79, 143}, {80, 144}, {81, 145}, {82, 146}, {83, 147}, {78, 128}, {111, 161}, {110, 160}, {95, 145}, {94, 144}, {79, 129}, {80, 130}, {113, 163}, {112, 162}, {93, 143}, {92, 142}, {89, 139}, {88, 138}, {85, 135}, {81, 131}, {84, 134}, {82, 132}, {114, 164}, {91, 141}, {90, 140}, {83, 133}, {86, 136}, {87, 137}, {64, 171}, {96, 146}, {109, 159}, {108, 158}, {105, 155}, {104, 154}, {101, 151}, {100, 150}, {97, 147}, {98, 148}, {107, 157}, {106, 156}, {99, 149}, {102, 152}, {103, 153} }>;

(II) A more general form is to represent the graph as the orbit of {57, 58} under the group generated by the following permutations:

a: (1, 58, 115)(2, 108, 164, 57, 65, 123)(3, 101, 156, 56, 72, 131)(4, 94, 148, 55, 79, 139)(5, 87, 140, 54, 86, 147)(6, 80, 132, 53, 93, 155)(7, 73, 124, 52, 100, 163)(8, 66, 116, 51, 107, 171)(9, 59, 165, 50, 114, 122)(10, 109, 157, 49, 64, 130)(11, 102, 149, 48, 71, 138)(12, 95, 141, 47, 78, 146)(13, 88, 133, 46, 85, 154)(14, 81, 125, 45, 92, 162)(15, 74, 117, 44, 99, 170)(16, 67, 166, 43, 106, 121)(17, 60, 158, 42, 113, 129)(18, 110, 150, 41, 63, 137)(19, 103, 142, 40, 70, 145)(20, 96, 134, 39, 77, 153)(21, 89, 126, 38, 84, 161)(22, 82, 118, 37, 91, 169)(23, 75, 167, 36, 98, 120)(24, 68, 159, 35, 105, 128)(25, 61, 151, 34, 112, 136)(26, 111, 143, 33, 62, 144)(27, 104, 135, 32, 69, 152)(28, 97, 127, 31, 76, 160)(29, 90, 119, 30, 83, 168)
b: (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, 169, 170, 171)
c: (2, 57)(3, 56)(4, 55)(5, 54)(6, 53)(7, 52)(8, 51)(9, 50)(10, 49)(11, 48)(12, 47)(13, 46)(14, 45)(15, 44)(16, 43)(17, 42)(18, 41)(19, 40)(20, 39)(21, 38)(22, 37)(23, 36)(24, 35)(25, 34)(26, 33)(27, 32)(28, 31)(29, 30)(59, 114)(60, 113)(61, 112)(62, 111)(63, 110)(64, 109)(65, 108)(66, 107)(67, 106)(68, 105)(69, 104)(70, 103)(71, 102)(72, 101)(73, 100)(74, 99)(75, 98)(76, 97)(77, 96)(78, 95)(79, 94)(80, 93)(81, 92)(82, 91)(83, 90)(84, 89)(85, 88)(86, 87)(116, 171)(117, 170)(118, 169)(119, 168)(120, 167)(121, 166)(122, 165)(123, 164)(124, 163)(125, 162)(126, 161)(127, 160)(128, 159)(129, 158)(130, 157)(131, 156)(132, 155)(133, 154)(134, 153)(135, 152)(136, 151)(137, 150)(138, 149)(139, 148)(140, 147)(141, 146)(142, 145)(143, 144)

(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[ 171, 7 ]
171
-1 123 59 114 164
-2 165 58 124 60
-3 166 59 125 61
-4 167 60 126 62
-5 168 61 127 63
-6 169 62 128 64
-7 170 63 129 65
-8 66 171 64 130
-9 67 115 65 131
-10 66 132 68 116
-11 67 133 69 117
-12 68 134 70 118
-13 69 135 71 119
-14 70 136 72 120
-15 121 71 137 73
-16 122 72 138 74
-17 123 73 139 75
-18 124 74 140 76
-19 77 125 75 141
-20 78 126 76 142
-21 77 143 79 127
-22 78 144 80 128
-23 79 145 81 129
-24 80 146 82 130
-25 81 147 83 131
-26 132 82 148 84
-27 133 83 149 85
-28 134 84 150 86
-29 135 85 151 87
-30 88 136 86 152
-31 89 137 87 153
-32 88 154 90 138
-33 89 155 91 139
-34 90 156 92 140
-35 91 157 93 141
-36 92 158 94 142
-37 143 93 159 95
-38 144 94 160 96
-39 145 95 161 97
-40 146 96 162 98
-41 99 147 97 163
-42 100 148 98 164
-43 99 165 101 149
-44 100 166 102 150
-45 101 167 103 151
-46 102 168 104 152
-47 103 169 105 153
-48 154 104 170 106
-49 155 105 171 107
-50 156 115 106 108
-51 157 116 107 109
-52 110 158 117 108
-53 111 159 118 109
-54 110 112 160 119
-55 111 113 161 120
-56 121 112 114 162
-57 122 58 113 163
-58 165 122 2 57
-59 1 166 123 3
-60 2 167 124 4
-61 3 168 125 5
-62 4 169 126 6
-63 5 170 127 7
-64 6 171 128 8
-65 115 7 129 9
-66 116 8 130 10
-67 11 117 9 131
-68 132 12 118 10
-69 11 133 13 119
-70 12 134 14 120
-71 121 13 135 15
-72 122 14 136 16
-73 123 15 137 17
-74 124 16 138 18
-75 125 17 139 19
-76 126 18 140 20
-77 127 19 141 21
-78 22 128 20 142
-79 143 23 129 21
-80 22 144 24 130
-81 23 145 25 131
-82 132 24 146 26
-83 133 25 147 27
-84 134 26 148 28
-85 135 27 149 29
-86 136 28 150 30
-87 137 29 151 31
-88 138 30 152 32
-89 33 139 31 153
-90 154 34 140 32
-91 33 155 35 141
-92 34 156 36 142
-93 143 35 157 37
-94 144 36 158 38
-95 145 37 159 39
-96 146 38 160 40
-97 147 39 161 41
-98 148 40 162 42
-99 149 41 163 43
-100 44 150 42 164
-101 165 45 151 43
-102 44 166 46 152
-103 45 167 47 153
-104 154 46 168 48
-105 155 47 169 49
-106 156 48 170 50
-107 157 49 171 51
-108 158 115 50 52
-109 159 116 51 53
-110 160 117 52 54
-111 55 161 118 53
-112 56 162 119 54
-113 55 57 163 120
-114 121 1 56 164
-115 50 9 108 65
-116 66 51 10 109
-117 11 110 67 52
-118 12 111 68 53
-119 13 112 69 54
-120 55 14 113 70
-121 56 15 114 71
-122 57 58 16 72
-123 1 59 17 73
-124 2 60 18 74
-125 3 61 19 75
-126 4 62 20 76
-127 77 5 63 21
-128 22 78 6 64
-129 23 79 7 65
-130 66 24 80 8
-131 67 25 81 9
-132 68 26 82 10
-133 11 69 27 83
-134 12 70 28 84
-135 13 71 29 85
-136 14 72 30 86
-137 15 73 31 87
-138 88 16 74 32
-139 33 89 17 75
-140 34 90 18 76
-141 77 35 91 19
-142 78 36 92 20
-143 79 37 93 21
-144 22 80 38 94
-145 23 81 39 95
-146 24 82 40 96
-147 25 83 41 97
-148 26 84 42 98
-149 99 27 85 43
-150 44 100 28 86
-151 45 101 29 87
-152 88 46 102 30
-153 89 47 103 31
-154 90 48 104 32
-155 33 91 49 105
-156 34 92 50 106
-157 35 93 51 107
-158 36 94 52 108
-159 37 95 53 109
-160 110 38 96 54
-161 55 111 39 97
-162 56 112 40 98
-163 99 57 113 41
-164 1 100 114 42
-165 2 101 58 43
-166 44 3 102 59
-167 45 4 103 60
-168 46 5 104 61
-169 47 6 105 62
-170 48 7 106 63
-171 49 8 107 64
0

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