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