Graph forms
for C4 [ 192, 74 ] = UG(ATD[192,1])
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On this page are computer-accessible forms for the graph C4[ 192, 74 ] =
UG(ATD[192,1]).
(I) Following is a form readable by MAGMA:
g:=Graph<192|{ {116, 117}, {154, 155}, {1, 3}, {172, 174}, {168, 170}, {41, 43},
{128, 130}, {1, 2}, {188, 191}, {4, 7}, {3, 6}, {2, 4}, {187, 189}, {99, 101},
{2, 5}, {185, 190}, {5, 13}, {167, 175}, {7, 15}, {6, 14}, {50, 59}, {118, 127},
{36, 46}, {51, 57}, {85, 95}, {3, 8}, {147, 152}, {67, 72}, {7, 12}, {98, 105},
{113, 122}, {4, 9}, {178, 191}, {144, 157}, {18, 31}, {16, 29}, {6, 11}, {5,
10}, {177, 190}, {150, 153}, {17, 30}, {103, 119}, {172, 188}, {162, 178}, {133,
148}, {171, 186}, {79, 93}, {169, 187}, {11, 24}, {64, 83}, {47, 60}, {15, 28},
{130, 145}, {104, 124}, {1, 20}, {168, 189}, {166, 179}, {162, 183}, {14, 27},
{12, 25}, {96, 118}, {161, 183}, {160, 182}, {101, 115}, {129, 151}, {131, 149},
{13, 26}, {8, 16}, {139, 147}, {12, 20}, {11, 19}, {10, 18}, {9, 17}, {77, 84},
{165, 188}, {100, 126}, {108, 118}, {78, 85}, {173, 182}, {163, 184}, {160,
187}, {44, 48}, {69, 89}, {75, 87}, {111, 115}, {8, 21}, {164, 185}, {65, 92},
{40, 53}, {10, 23}, {32, 62}, {35, 61}, {33, 63}, {9, 22}, {170, 181}, {142,
145}, {71, 88}, {128, 159}, {142, 174}, {154, 186}, {148, 180}, {1, 32}, {140,
173}, {21, 52}, {129, 160}, {23, 53}, {31, 61}, {30, 60}, {27, 57}, {26, 56},
{82, 113}, {139, 168}, {132, 167}, {135, 164}, {72, 108}, {73, 109}, {74, 110},
{75, 111}, {64, 101}, {157, 184}, {66, 103}, {132, 161}, {134, 163}, {28, 58},
{150, 176}, {29, 59}, {65, 102}, {151, 176}, {73, 110}, {88, 127}, {133, 162},
{80, 120}, {81, 121}, {85, 125}, {86, 126}, {84, 125}, {152, 177}, {137, 160},
{91, 113}, {159, 181}, {158, 180}, {67, 104}, {154, 177}, {128, 171}, {135,
172}, {13, 33}, {141, 161}, {68, 104}, {31, 51}, {30, 50}, {29, 49}, {28, 48},
{15, 35}, {14, 34}, {69, 105}, {70, 106}, {71, 107}, {81, 124}, {138, 167},
{136, 165}, {24, 54}, {157, 179}, {156, 178}, {151, 185}, {25, 55}, {136, 166},
{93, 114}, {137, 166}, {68, 116}, {69, 117}, {70, 118}, {2, 51}, {155, 170},
{149, 164}, {66, 115}, {22, 39}, {80, 97}, {81, 96}, {74, 120}, {145, 163}, {75,
121}, {19, 32}, {65, 114}, {89, 106}, {16, 36}, {153, 173}, {27, 47}, {26, 46},
{25, 45}, {24, 44}, {19, 39}, {18, 38}, {17, 37}, {83, 102}, {87, 98}, {76,
122}, {77, 123}, {82, 101}, {146, 171}, {25, 34}, {148, 175}, {20, 40}, {149,
169}, {144, 172}, {23, 43}, {22, 42}, {21, 41}, {92, 96}, {72, 119}, {52, 112},
{4, 77}, {56, 113}, {58, 112}, {3, 76}, {58, 109}, {60, 107}, {57, 96}, {62,
103}, {61, 100}, {62, 100}, {58, 97}, {60, 98}, {61, 99}, {63, 94}, {34, 64},
{35, 65}, {39, 68}, {38, 67}, {47, 74}, {45, 72}, {37, 66}, {46, 73}, {5, 109},
{55, 95}, {54, 94}, {53, 93}, {52, 92}, {51, 91}, {50, 90}, {49, 89}, {48, 88},
{7, 111}, {6, 110}, {37, 76}, {36, 79}, {38, 74}, {43, 71}, {42, 70}, {40, 69},
{55, 90}, {33, 78}, {54, 89}, {62, 79}, {179, 192}, {11, 127}, {180, 192}, {8,
125}, {39, 80}, {59, 67}, {21, 108}, {46, 87}, {44, 85}, {42, 83}, {40, 81},
{41, 82}, {48, 75}, {45, 86}, {49, 76}, {63, 66}, {56, 70}, {43, 84}, {50, 77},
{47, 174}, {12, 142}, {34, 161}, {56, 188}, {9, 140}, {26, 159}, {24, 158}, {54,
176}, {53, 179}, {49, 183}, {10, 141}, {27, 156}, {13, 138}, {36, 173}, {55,
190}, {73, 192}, {18, 152}, {59, 181}, {57, 182}, {52, 164}, {63, 174}, {44,
184}, {16, 134}, {38, 176}, {35, 181}, {32, 185}, {42, 177}, {14, 146}, {37,
186}, {31, 184}, {15, 165}, {33, 139}, {28, 183}, {30, 175}, {19, 167}, {29,
169}, {22, 163}, {17, 166}, {20, 168}, {23, 171}, {41, 150}, {78, 143}, {112,
186}, {95, 144}, {83, 131}, {117, 165}, {88, 137}, {126, 170}, {119, 162}, {124,
169}, {86, 143}, {86, 140}, {90, 128}, {91, 129}, {90, 129}, {95, 132}, {94,
130}, {94, 131}, {91, 133}, {93, 130}, {126, 158}, {127, 159}, {120, 153}, {122,
155}, {124, 157}, {104, 138}, {105, 139}, {108, 142}, {117, 151}, {100, 135},
{120, 155}, {121, 154}, {97, 133}, {98, 134}, {99, 134}, {121, 156}, {123, 158},
{82, 180}, {106, 140}, {107, 141}, {110, 136}, {116, 146}, {106, 141}, {123,
156}, {87, 190}, {122, 144}, {84, 191}, {114, 153}, {107, 135}, {45, 192}, {80,
189}, {102, 136}, {103, 137}, {125, 147}, {119, 152}, {97, 145}, {99, 146}, {92,
175}, {102, 147}, {114, 132}, {78, 182}, {109, 149}, {123, 131}, {111, 150},
{115, 138}, {71, 189}, {64, 187}, {68, 191}, {116, 143}, {79, 178}, {105, 148},
{112, 143} }>;
(II) A more general form is to represent the graph as the orbit of {116, 117}
under the group generated by the following permutations:
a: (1, 2, 4, 7, 12, 20)(3, 5, 9, 15, 25, 40)(6, 10, 17, 28, 45, 69)(8, 13, 22,
35, 55, 81)(11, 18, 30, 48, 72, 105)(14, 23, 37, 58, 86, 117)(16, 26, 42, 65,
95, 124)(19, 31, 50, 75, 108, 139)(21, 33, 39, 61, 90, 121)(24, 38, 60, 88, 119,
148)(27, 43, 66, 97, 126, 151)(29, 46, 70, 102, 132, 157)(32, 51, 77, 111, 142,
168)(34, 53, 76, 109, 140, 165)(36, 56, 83, 114, 144, 169)(41, 63, 80, 100, 129,
156)(44, 67, 98, 127, 152, 175)(47, 71, 103, 133, 158, 176)(49, 73, 106, 136,
161, 179)(52, 78, 68, 99, 128, 154)(54, 74, 107, 137, 162, 180)(57, 84, 115,
145, 170, 185)(59, 87, 118, 147, 167, 184)(62, 91, 123, 150, 174, 189)(64, 93,
122, 149, 173, 188)(79, 113, 131, 153, 172, 187)(82, 94, 120, 135, 160, 178)(85,
104, 134, 159, 177, 92)(89, 110, 141, 166, 183, 192)(96, 125, 138, 163, 181,
190)(101, 130, 155, 164, 182, 191)(112, 143, 116, 146, 171, 186) (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 **************
b: (2, 3)(4, 6)(5, 8)(7, 11)(9, 14)(10, 16)(12, 19)(13, 21)(15, 24)(17, 27)(18,
29)(20, 32)(22, 34)(23, 36)(25, 39)(26, 41)(28, 44)(30, 47)(31, 49)(33, 52)(35,
54)(37, 57)(38, 59)(40, 62)(42, 64)(43, 46)(45, 68)(50, 74)(51, 76)(53, 79)(55,
80)(56, 82)(58, 85)(61, 89)(63, 92)(65, 94)(66, 96)(69, 100)(70, 101)(71,
87)(72, 104)(73, 84)(75, 88)(77, 110)(78, 112)(81, 103)(86, 116)(90, 120)(91,
122)(95, 97)(98, 107)(99, 106)(102, 131)(105, 135)(108, 138)(109, 125)(111,
127)(114, 130)(115, 118)(117, 126)(119, 124)(121, 137)(123, 136)(128, 153)(129,
155)(132, 145)(133, 144)(134, 141)(139, 164)(140, 146)(142, 167)(147, 149)(148,
172)(150, 159)(151, 170)(152, 169)(154, 160)(156, 166)(157, 162)(158, 165)(161,
163)(168, 185)(171, 173)(174, 175)(176, 181)(177, 187)(178, 179)(180, 188)(182,
186)(183, 184)(189, 190)(191, 192)
C4[ 192, 74 ]
192
-1 2 3 20 32
-2 1 4 5 51
-3 1 6 8 76
-4 77 2 7 9
-5 2 13 10 109
-6 11 110 3 14
-7 12 111 4 15
-8 3 125 16 21
-9 22 4 17 140
-10 23 5 18 141
-11 24 6 127 19
-12 25 7 20 142
-13 33 26 5 138
-14 34 146 27 6
-15 165 35 28 7
-16 134 36 29 8
-17 166 37 30 9
-18 38 31 152 10
-19 11 167 39 32
-20 1 12 168 40
-21 8 41 52 108
-22 39 9 42 163
-23 171 53 10 43
-24 11 44 158 54
-25 55 12 34 45
-26 56 13 46 159
-27 57 156 14 47
-28 58 15 48 183
-29 59 169 16 49
-30 60 17 50 175
-31 61 18 51 184
-32 1 62 19 185
-33 78 13 139 63
-34 14 25 161 64
-35 15 181 61 65
-36 46 79 16 173
-37 66 17 76 186
-38 176 67 18 74
-39 22 68 80 19
-40 69 81 20 53
-41 82 150 21 43
-42 22 177 70 83
-43 23 71 84 41
-44 24 48 85 184
-45 25 192 72 86
-46 36 26 73 87
-47 27 60 74 174
-48 44 88 28 75
-49 89 29 183 76
-50 77 90 59 30
-51 2 57 91 31
-52 112 92 21 164
-53 23 179 93 40
-54 176 89 24 94
-55 90 25 190 95
-56 188 113 26 70
-57 27 182 51 96
-58 112 28 97 109
-59 67 181 50 29
-60 47 30 107 98
-61 99 100 35 31
-62 100 79 103 32
-63 33 66 94 174
-64 187 34 101 83
-65 35 102 92 114
-66 37 103 115 63
-67 59 38 104 72
-68 191 104 39 116
-69 89 105 40 117
-70 56 106 118 42
-71 88 189 107 43
-72 45 67 108 119
-73 110 46 192 109
-74 110 47 38 120
-75 121 111 48 87
-76 122 3 37 49
-77 123 4 50 84
-78 33 143 182 85
-79 178 36 93 62
-80 189 39 97 120
-81 121 124 40 96
-82 101 113 180 41
-83 102 42 64 131
-84 77 125 191 43
-85 44 78 125 95
-86 143 45 126 140
-87 46 190 75 98
-88 48 71 137 127
-89 69 49 106 54
-90 55 50 128 129
-91 133 113 51 129
-92 52 96 65 175
-93 79 114 53 130
-94 63 130 54 131
-95 55 132 144 85
-96 57 81 92 118
-97 133 145 58 80
-98 134 60 105 87
-99 101 134 146 61
-100 135 126 61 62
-101 99 82 115 64
-102 136 147 83 65
-103 66 137 62 119
-104 67 68 124 138
-105 69 148 139 98
-106 89 70 140 141
-107 135 60 71 141
-108 72 118 21 142
-109 58 5 149 73
-110 136 6 73 74
-111 115 7 150 75
-112 143 58 52 186
-113 56 122 91 82
-114 132 93 65 153
-115 66 111 101 138
-116 143 68 146 117
-117 165 69 116 151
-118 70 127 96 108
-119 103 72 162 152
-120 155 80 74 153
-121 154 156 81 75
-122 144 155 113 76
-123 77 156 158 131
-124 157 81 169 104
-125 147 84 8 85
-126 100 158 170 86
-127 11 88 159 118
-128 90 159 171 130
-129 90 91 160 151
-130 145 93 94 128
-131 123 83 94 149
-132 167 114 95 161
-133 91 148 162 97
-134 99 16 163 98
-135 100 172 107 164
-136 110 165 166 102
-137 88 166 103 160
-138 13 167 104 115
-139 33 168 147 105
-140 106 173 9 86
-141 106 161 107 10
-142 12 145 108 174
-143 78 112 116 86
-144 122 157 95 172
-145 97 130 163 142
-146 99 14 116 171
-147 102 125 139 152
-148 133 180 105 175
-149 169 109 131 164
-150 176 111 41 153
-151 176 117 129 185
-152 177 147 18 119
-153 114 150 173 120
-154 121 155 177 186
-155 154 122 170 120
-156 121 123 178 27
-157 144 124 179 184
-158 24 123 180 126
-159 26 181 127 128
-160 187 137 182 129
-161 132 34 183 141
-162 133 178 183 119
-163 22 134 145 184
-164 135 149 52 185
-165 188 15 136 117
-166 179 136 137 17
-167 132 138 19 175
-168 189 170 139 20
-169 187 124 149 29
-170 155 168 126 181
-171 23 146 128 186
-172 144 188 135 174
-173 36 182 140 153
-174 47 172 63 142
-175 167 92 148 30
-176 38 150 151 54
-177 154 190 42 152
-178 79 156 191 162
-179 166 157 192 53
-180 158 82 148 192
-181 35 59 159 170
-182 78 57 160 173
-183 49 28 161 162
-184 44 157 31 163
-185 190 151 32 164
-186 154 112 37 171
-187 189 169 160 64
-188 165 56 191 172
-189 187 80 168 71
-190 55 177 185 87
-191 188 68 178 84
-192 45 179 180 73
0