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