[Home] [Table] [Glossary] [Families]

On this page are computer-accessible forms for the graph C4[ 174, 3 ] = PS(6,29;12).

(I) Following is a form readable by MAGMA:

g:=Graph<174|{ {29, 30}, {145, 146}, {48, 60}, {51, 63}, {50, 62}, {49, 61}, {112, 124}, {113, 125}, {114, 126}, {115, 127}, {87, 88}, {42, 59}, {46, 63}, {44, 61}, {100, 117}, {102, 119}, {104, 121}, {106, 123}, {108, 125}, {110, 127}, {45, 62}, {101, 118}, {105, 122}, {109, 126}, {47, 59}, {108, 120}, {109, 121}, {110, 122}, {111, 123}, {43, 60}, {107, 124}, {2, 30}, {131, 159}, {130, 158}, {129, 157}, {128, 156}, {65, 93}, {64, 92}, {3, 31}, {66, 94}, {67, 95}, {105, 117}, {106, 118}, {107, 119}, {1, 31}, {129, 159}, {128, 158}, {65, 95}, {64, 94}, {103, 120}, {2, 32}, {143, 173}, {142, 172}, {139, 169}, {138, 168}, {135, 165}, {134, 164}, {131, 161}, {130, 160}, {27, 57}, {3, 33}, {6, 36}, {7, 37}, {10, 40}, {11, 41}, {14, 44}, {15, 45}, {18, 48}, {19, 49}, {22, 52}, {23, 53}, {26, 56}, {66, 96}, {67, 97}, {70, 100}, {71, 101}, {74, 104}, {75, 105}, {78, 108}, {79, 109}, {82, 112}, {83, 113}, {86, 116}, {4, 32}, {143, 171}, {142, 170}, {141, 169}, {140, 168}, {135, 163}, {134, 162}, {133, 161}, {132, 160}, {29, 57}, {28, 56}, {5, 33}, {6, 34}, {7, 35}, {12, 40}, {13, 41}, {14, 42}, {15, 43}, {20, 48}, {21, 49}, {22, 50}, {23, 51}, {68, 96}, {69, 97}, {70, 98}, {71, 99}, {76, 104}, {77, 105}, {78, 106}, {79, 107}, {84, 112}, {85, 113}, {86, 114}, {87, 115}, {4, 34}, {141, 171}, {140, 170}, {133, 163}, {132, 162}, {28, 58}, {5, 35}, {12, 42}, {13, 43}, {20, 50}, {21, 51}, {68, 98}, {69, 99}, {76, 106}, {77, 107}, {84, 114}, {85, 115}, {8, 36}, {139, 167}, {138, 166}, {137, 165}, {136, 164}, {27, 55}, {9, 37}, {10, 38}, {11, 39}, {24, 52}, {25, 53}, {26, 54}, {72, 100}, {73, 101}, {74, 102}, {75, 103}, {8, 38}, {137, 167}, {136, 166}, {9, 39}, {24, 54}, {25, 55}, {72, 102}, {73, 103}, {1, 58}, {16, 44}, {145, 173}, {144, 172}, {17, 45}, {18, 46}, {19, 47}, {80, 108}, {81, 109}, {82, 110}, {83, 111}, {16, 46}, {144, 174}, {17, 47}, {80, 110}, {81, 111}, {59, 116}, {30, 76}, {31, 77}, {31, 72}, {30, 71}, {59, 89}, {63, 93}, {62, 92}, {60, 88}, {63, 91}, {62, 90}, {61, 89}, {60, 90}, {61, 91}, {32, 73}, {38, 79}, {36, 77}, {34, 75}, {33, 74}, {37, 78}, {32, 78}, {33, 79}, {35, 76}, {47, 64}, {48, 65}, {58, 75}, {56, 73}, {54, 71}, {52, 69}, {50, 67}, {34, 80}, {39, 85}, {38, 84}, {35, 81}, {49, 66}, {57, 74}, {53, 70}, {52, 64}, {55, 67}, {54, 66}, {53, 65}, {36, 82}, {37, 83}, {39, 80}, {51, 68}, {40, 81}, {46, 87}, {44, 85}, {42, 83}, {41, 82}, {45, 86}, {56, 68}, {58, 70}, {57, 69}, {40, 86}, {41, 87}, {43, 84}, {55, 72}, {18, 146}, {29, 157}, {28, 156}, {27, 155}, {19, 147}, {20, 148}, {21, 149}, {22, 150}, {23, 151}, {24, 152}, {25, 153}, {26, 154}, {16, 149}, {26, 159}, {18, 151}, {24, 157}, {17, 150}, {25, 158}, {19, 152}, {23, 156}, {20, 153}, {22, 155}, {21, 154}, {15, 148}, {2, 159}, {14, 147}, {1, 158}, {13, 146}, {1, 163}, {4, 166}, {5, 167}, {8, 170}, {9, 171}, {12, 174}, {3, 160}, {7, 164}, {11, 168}, {15, 172}, {4, 161}, {6, 163}, {12, 169}, {14, 171}, {2, 164}, {3, 165}, {10, 172}, {11, 173}, {5, 162}, {13, 170}, {8, 165}, {10, 167}, {6, 168}, {7, 169}, {9, 166}, {27, 160}, {16, 173}, {28, 161}, {17, 174}, {29, 162}, {90, 136}, {91, 137}, {94, 140}, {95, 141}, {92, 138}, {93, 139}, {95, 136}, {88, 129}, {90, 131}, {92, 133}, {94, 135}, {89, 130}, {93, 134}, {117, 174}, {88, 134}, {89, 135}, {91, 132}, {118, 148}, {127, 157}, {119, 149}, {122, 152}, {123, 153}, {126, 156}, {118, 146}, {119, 147}, {124, 152}, {125, 153}, {126, 154}, {127, 155}, {117, 147}, {124, 154}, {125, 155}, {96, 137}, {98, 139}, {100, 141}, {102, 143}, {97, 138}, {101, 142}, {120, 148}, {121, 149}, {122, 150}, {123, 151}, {96, 142}, {97, 143}, {120, 150}, {121, 151}, {99, 140}, {111, 128}, {112, 129}, {114, 131}, {116, 133}, {98, 144}, {99, 145}, {113, 130}, {116, 128}, {103, 144}, {115, 132}, {104, 145} }>;

(II) A more general form is to represent the graph as the orbit of {29, 30} under the group generated by the following permutations:

a: (1, 30)(2, 31)(3, 32)(4, 33)(5, 34)(6, 35)(7, 36)(8, 37)(9, 38)(10, 39)(11, 40)(12, 41)(13, 42)(14, 43)(15, 44)(16, 45)(17, 46)(18, 47)(19, 48)(20, 49)(21, 50)(22, 51)(23, 52)(24, 53)(25, 54)(26, 55)(27, 56)(28, 57)(29, 58)(59, 146)(60, 147)(61, 148)(62, 149)(63, 150)(64, 151)(65, 152)(66, 153)(67, 154)(68, 155)(69, 156)(70, 157)(71, 158)(72, 159)(73, 160)(74, 161)(75, 162)(76, 163)(77, 164)(78, 165)(79, 166)(80, 167)(81, 168)(82, 169)(83, 170)(84, 171)(85, 172)(86, 173)(87, 174)(88, 117)(89, 118)(90, 119)(91, 120)(92, 121)(93, 122)(94, 123)(95, 124)(96, 125)(97, 126)(98, 127)(99, 128)(100, 129)(101, 130)(102, 131)(103, 132)(104, 133)(105, 134)(106, 135)(107, 136)(108, 137)(109, 138)(110, 139)(111, 140)(112, 141)(113, 142)(114, 143)(115, 144)(116, 145)
b: (2, 13, 29, 18)(3, 25, 28, 6)(4, 8, 27, 23)(5, 20, 26, 11)(7, 15, 24, 16)(9, 10, 22, 21)(12, 17, 19, 14)(30, 146)(31, 158, 58, 163)(32, 170, 57, 151)(33, 153, 56, 168)(34, 165, 55, 156)(35, 148, 54, 173)(36, 160, 53, 161)(37, 172, 52, 149)(38, 155, 51, 166)(39, 167, 50, 154)(40, 150, 49, 171)(41, 162, 48, 159)(42, 174, 47, 147)(43, 157, 46, 164)(44, 169, 45, 152)(59, 117)(60, 129, 87, 134)(61, 141, 86, 122)(62, 124, 85, 139)(63, 136, 84, 127)(64, 119, 83, 144)(65, 131, 82, 132)(66, 143, 81, 120)(67, 126, 80, 137)(68, 138, 79, 125)(69, 121, 78, 142)(70, 133, 77, 130)(71, 145, 76, 118)(72, 128, 75, 135)(73, 140, 74, 123)(89, 100, 116, 105)(90, 112, 115, 93)(91, 95, 114, 110)(92, 107, 113, 98)(94, 102, 111, 103)(96, 97, 109, 108)(99, 104, 106, 101)
c: (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, 172, 173, 174)

(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.

**************

&Graph
C4[ 174, 3 ]
174
-1 58 158 31 163
-2 159 30 32 164
-3 33 165 160 31
-4 34 166 161 32
-5 33 35 167 162
-6 34 36 168 163
-7 35 37 169 164
-8 165 36 38 170
-9 166 37 39 171
-10 167 38 40 172
-11 168 39 41 173
-12 169 40 42 174
-13 146 170 41 43
-14 44 147 171 42
-15 45 148 172 43
-16 44 46 149 173
-17 45 47 150 174
-18 46 146 48 151
-19 47 147 49 152
-20 48 148 50 153
-21 154 49 149 51
-22 155 50 150 52
-23 156 51 151 53
-24 157 52 152 54
-25 55 158 53 153
-26 154 56 159 54
-27 55 155 57 160
-28 56 156 58 161
-29 57 157 30 162
-30 2 71 29 76
-31 77 1 3 72
-32 78 2 4 73
-33 79 3 5 74
-34 80 4 6 75
-35 81 5 7 76
-36 77 82 6 8
-37 78 83 7 9
-38 79 84 8 10
-39 11 80 85 9
-40 12 81 86 10
-41 11 13 82 87
-42 12 14 59 83
-43 13 15 60 84
-44 14 16 61 85
-45 15 17 62 86
-46 16 18 63 87
-47 59 17 19 64
-48 60 18 20 65
-49 66 61 19 21
-50 22 67 62 20
-51 23 68 63 21
-52 22 24 69 64
-53 23 25 70 65
-54 66 24 26 71
-55 67 25 27 72
-56 68 26 28 73
-57 69 27 29 74
-58 1 70 28 75
-59 89 47 116 42
-60 88 90 48 43
-61 44 89 91 49
-62 45 90 92 50
-63 46 91 93 51
-64 47 92 94 52
-65 48 93 95 53
-66 49 94 96 54
-67 55 50 95 97
-68 56 51 96 98
-69 99 57 52 97
-70 100 58 53 98
-71 99 101 30 54
-72 55 100 102 31
-73 56 101 103 32
-74 33 57 102 104
-75 34 58 103 105
-76 35 104 106 30
-77 36 105 107 31
-78 37 106 108 32
-79 33 38 107 109
-80 110 34 39 108
-81 111 35 40 109
-82 110 112 36 41
-83 111 113 37 42
-84 112 114 38 43
-85 44 113 115 39
-86 45 114 116 40
-87 88 46 115 41
-88 134 60 129 87
-89 135 59 61 130
-90 136 60 62 131
-91 132 137 61 63
-92 133 138 62 64
-93 134 139 63 65
-94 66 135 140 64
-95 67 136 141 65
-96 66 68 137 142
-97 143 67 69 138
-98 144 68 70 139
-99 145 69 71 140
-100 70 72 117 141
-101 71 73 118 142
-102 143 72 74 119
-103 144 73 75 120
-104 121 145 74 76
-105 77 122 117 75
-106 78 123 118 76
-107 77 79 124 119
-108 78 80 125 120
-109 121 79 81 126
-110 122 80 82 127
-111 123 81 83 128
-112 124 82 84 129
-113 125 83 85 130
-114 126 84 86 131
-115 132 127 85 87
-116 133 59 128 86
-117 100 147 105 174
-118 101 146 148 106
-119 102 147 149 107
-120 103 148 150 108
-121 104 149 151 109
-122 110 105 150 152
-123 111 106 151 153
-124 154 112 107 152
-125 155 113 108 153
-126 154 156 114 109
-127 110 155 157 115
-128 111 156 158 116
-129 88 112 157 159
-130 89 113 158 160
-131 90 114 159 161
-132 91 115 160 162
-133 92 116 161 163
-134 88 93 162 164
-135 165 89 94 163
-136 166 90 95 164
-137 165 167 91 96
-138 166 168 92 97
-139 167 169 93 98
-140 99 168 170 94
-141 100 169 171 95
-142 101 170 172 96
-143 102 171 173 97
-144 103 172 174 98
-145 99 146 104 173
-146 13 145 18 118
-147 14 117 19 119
-148 15 118 20 120
-149 121 16 119 21
-150 22 122 17 120
-151 121 23 123 18
-152 122 24 124 19
-153 123 25 125 20
-154 124 26 126 21
-155 22 125 27 127
-156 23 126 28 128
-157 24 127 29 129
-158 1 25 128 130
-159 2 26 129 131
-160 132 3 27 130
-161 133 4 28 131
-162 132 134 5 29
-163 1 133 135 6
-164 2 134 136 7
-165 3 135 137 8
-166 4 136 138 9
-167 5 137 139 10
-168 11 6 138 140
-169 12 7 139 141
-170 13 8 140 142
-171 143 14 9 141
-172 144 15 10 142
-173 11 143 145 16
-174 12 144 17 117
0

**************