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