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