Graph forms
for C4 [ 165, 3 ] = C_165(1,76)
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On this page are computer-accessible forms for the graph C4[ 165, 3 ] =
C_165(1,76).
(I) Following is a form readable by MAGMA:
g:=Graph<165|{ {2, 3}, {164, 165}, {162, 163}, {160, 161}, {158, 159}, {156,
157}, {154, 155}, {152, 153}, {150, 151}, {148, 149}, {146, 147}, {144, 145},
{142, 143}, {140, 141}, {138, 139}, {136, 137}, {134, 135}, {132, 133}, {130,
131}, {128, 129}, {126, 127}, {124, 125}, {122, 123}, {120, 121}, {118, 119},
{116, 117}, {114, 115}, {112, 113}, {110, 111}, {108, 109}, {52, 53}, {50, 51},
{48, 49}, {46, 47}, {44, 45}, {42, 43}, {40, 41}, {38, 39}, {36, 37}, {34, 35},
{4, 5}, {6, 7}, {8, 9}, {10, 11}, {12, 13}, {14, 15}, {16, 17}, {18, 19}, {20,
21}, {22, 23}, {24, 25}, {26, 27}, {28, 29}, {30, 31}, {32, 33}, {54, 55}, {56,
57}, {58, 59}, {60, 61}, {62, 63}, {64, 65}, {66, 67}, {68, 69}, {70, 71}, {72,
73}, {74, 75}, {76, 77}, {78, 79}, {80, 81}, {82, 83}, {84, 85}, {86, 87}, {88,
89}, {90, 91}, {92, 93}, {94, 95}, {96, 97}, {98, 99}, {100, 101}, {102, 103},
{104, 105}, {106, 107}, {1, 2}, {161, 162}, {157, 158}, {153, 154}, {149, 150},
{145, 146}, {141, 142}, {137, 138}, {133, 134}, {129, 130}, {125, 126}, {121,
122}, {117, 118}, {113, 114}, {109, 110}, {53, 54}, {49, 50}, {45, 46}, {41,
42}, {37, 38}, {33, 34}, {5, 6}, {9, 10}, {13, 14}, {17, 18}, {21, 22}, {25,
26}, {29, 30}, {57, 58}, {61, 62}, {65, 66}, {69, 70}, {73, 74}, {77, 78}, {81,
82}, {85, 86}, {89, 90}, {93, 94}, {97, 98}, {101, 102}, {105, 106}, {3, 4},
{163, 164}, {155, 156}, {147, 148}, {139, 140}, {131, 132}, {123, 124}, {115,
116}, {51, 52}, {43, 44}, {35, 36}, {11, 12}, {19, 20}, {27, 28}, {59, 60}, {67,
68}, {75, 76}, {83, 84}, {91, 92}, {99, 100}, {107, 108}, {7, 8}, {151, 152},
{135, 136}, {119, 120}, {39, 40}, {23, 24}, {55, 56}, {71, 72}, {87, 88}, {103,
104}, {15, 16}, {143, 144}, {111, 112}, {47, 48}, {79, 80}, {31, 32}, {159,
160}, {95, 96}, {1, 77}, {51, 127}, {50, 126}, {49, 125}, {48, 124}, {35, 111},
{34, 110}, {33, 109}, {2, 78}, {3, 79}, {16, 92}, {17, 93}, {18, 94}, {19, 95},
{32, 108}, {4, 80}, {47, 123}, {46, 122}, {45, 121}, {44, 120}, {39, 115}, {38,
114}, {37, 113}, {36, 112}, {5, 81}, {6, 82}, {7, 83}, {12, 88}, {13, 89}, {14,
90}, {15, 91}, {2, 91}, {38, 127}, {36, 125}, {34, 123}, {32, 121}, {4, 93}, {6,
95}, {1, 90}, {37, 126}, {33, 122}, {5, 94}, {8, 84}, {43, 119}, {42, 118}, {41,
117}, {40, 116}, {9, 85}, {10, 86}, {11, 87}, {3, 92}, {35, 124}, {7, 96}, {15,
104}, {23, 112}, {31, 120}, {8, 97}, {10, 99}, {12, 101}, {14, 103}, {24, 113},
{26, 115}, {28, 117}, {30, 119}, {9, 98}, {13, 102}, {25, 114}, {29, 118}, {11,
100}, {27, 116}, {20, 96}, {21, 97}, {22, 98}, {23, 99}, {28, 104}, {29, 105},
{30, 106}, {31, 107}, {16, 105}, {18, 107}, {20, 109}, {22, 111}, {17, 106},
{21, 110}, {24, 100}, {25, 101}, {26, 102}, {27, 103}, {19, 108}, {63, 64}, {1,
165}, {39, 128}, {47, 136}, {55, 144}, {63, 152}, {40, 129}, {46, 135}, {44,
133}, {42, 131}, {56, 145}, {58, 147}, {60, 149}, {62, 151}, {41, 130}, {45,
134}, {57, 146}, {61, 150}, {43, 132}, {59, 148}, {52, 128}, {53, 129}, {54,
130}, {55, 131}, {60, 136}, {61, 137}, {62, 138}, {63, 139}, {48, 137}, {52,
141}, {50, 139}, {54, 143}, {49, 138}, {53, 142}, {56, 132}, {57, 133}, {58,
134}, {59, 135}, {51, 140}, {64, 140}, {65, 141}, {66, 142}, {67, 143}, {80,
156}, {81, 157}, {82, 158}, {83, 159}, {68, 144}, {69, 145}, {70, 146}, {71,
147}, {76, 152}, {77, 153}, {78, 154}, {79, 155}, {64, 153}, {66, 155}, {68,
157}, {70, 159}, {65, 154}, {69, 158}, {72, 148}, {73, 149}, {74, 150}, {75,
151}, {67, 156}, {71, 160}, {72, 161}, {74, 163}, {76, 165}, {73, 162}, {75,
164}, {84, 160}, {85, 161}, {86, 162}, {87, 163}, {88, 164}, {89, 165}, {127,
128} }>;
(II) A more general form is to represent the graph as the orbit of {2, 3}
under the group generated by the following permutations:
a: (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41,
42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61,
62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81,
82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100,
101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116,
117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132,
133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148,
149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164,
165) (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, 90)(3, 14)(4, 103)(5, 27)(6, 116)(7, 40)(8, 129)(9, 53)(10, 142)(11,
66)(12, 155)(13, 79)(15, 92)(17, 105)(18, 29)(19, 118)(20, 42)(21, 131)(22,
55)(23, 144)(24, 68)(25, 157)(26, 81)(28, 94)(30, 107)(32, 120)(33, 44)(34,
133)(35, 57)(36, 146)(37, 70)(38, 159)(39, 83)(41, 96)(43, 109)(45, 122)(47,
135)(48, 59)(49, 148)(50, 72)(51, 161)(52, 85)(54, 98)(56, 111)(58, 124)(60,
137)(62, 150)(63, 74)(64, 163)(65, 87)(67, 100)(69, 113)(71, 126)(73, 139)(75,
152)(77, 165)(78, 89)(80, 102)(82, 115)(84, 128)(86, 141)(88, 154)(93, 104)(95,
117)(97, 130)(99, 143)(101, 156)(108, 119)(110, 132)(112, 145)(114, 158)(123,
134)(125, 147)(127, 160)(138, 149)(140, 162)(153, 164)
c: (2, 77)(3, 153)(4, 64)(5, 140)(6, 51)(7, 127)(8, 38)(9, 114)(10, 25)(11,
101)(13, 88)(14, 164)(15, 75)(16, 151)(17, 62)(18, 138)(19, 49)(20, 125)(21,
36)(22, 112)(24, 99)(26, 86)(27, 162)(28, 73)(29, 149)(30, 60)(31, 136)(32,
47)(33, 123)(35, 110)(37, 97)(39, 84)(40, 160)(41, 71)(42, 147)(43, 58)(44,
134)(46, 121)(48, 108)(50, 95)(52, 82)(53, 158)(54, 69)(55, 145)(57, 132)(59,
119)(61, 106)(63, 93)(65, 80)(66, 156)(68, 143)(70, 130)(72, 117)(74, 104)(76,
91)(79, 154)(81, 141)(83, 128)(85, 115)(87, 102)(90, 165)(92, 152)(94, 139)(96,
126)(98, 113)(103, 163)(105, 150)(107, 137)(109, 124)(116, 161)(118, 148)(120,
135)(129, 159)(131, 146)(142, 157)
C4[ 165, 3 ]
165
-1 77 165 2 90
-2 1 78 3 91
-3 2 79 4 92
-4 3 80 5 93
-5 4 81 6 94
-6 5 82 7 95
-7 6 83 8 96
-8 7 84 9 97
-9 8 85 10 98
-10 11 99 9 86
-11 12 100 10 87
-12 11 88 13 101
-13 12 89 14 102
-14 13 90 15 103
-15 14 91 16 104
-16 15 92 17 105
-17 16 93 18 106
-18 17 94 19 107
-19 18 95 20 108
-20 19 96 21 109
-21 22 110 20 97
-22 23 111 21 98
-23 22 99 24 112
-24 23 100 25 113
-25 24 101 26 114
-26 25 102 27 115
-27 26 103 28 116
-28 27 104 29 117
-29 28 105 30 118
-30 29 106 31 119
-31 30 107 32 120
-32 33 121 31 108
-33 34 122 32 109
-34 33 110 35 123
-35 34 111 36 124
-36 35 112 37 125
-37 36 113 38 126
-38 37 114 39 127
-39 38 115 40 128
-40 39 116 41 129
-41 40 117 42 130
-42 41 118 43 131
-43 44 132 42 119
-44 45 133 43 120
-45 44 121 46 134
-46 45 122 47 135
-47 46 123 48 136
-48 47 124 49 137
-49 48 125 50 138
-50 49 126 51 139
-51 50 127 52 140
-52 51 128 53 141
-53 52 129 54 142
-54 55 143 53 130
-55 56 144 54 131
-56 55 132 57 145
-57 56 133 58 146
-58 57 134 59 147
-59 58 135 60 148
-60 59 136 61 149
-61 60 137 62 150
-62 61 138 63 151
-63 62 139 64 152
-64 63 140 65 153
-65 66 154 64 141
-66 67 155 65 142
-67 66 143 68 156
-68 67 144 69 157
-69 68 145 70 158
-70 69 146 71 159
-71 70 147 72 160
-72 71 148 73 161
-73 72 149 74 162
-74 73 150 75 163
-75 74 151 76 164
-76 77 165 75 152
-77 1 78 76 153
-78 77 154 2 79
-79 78 155 3 80
-80 79 156 4 81
-81 80 157 5 82
-82 81 158 6 83
-83 82 159 7 84
-84 83 160 8 85
-85 84 161 9 86
-86 85 162 10 87
-87 11 88 86 163
-88 12 89 87 164
-89 88 165 13 90
-90 1 89 14 91
-91 2 90 15 92
-92 3 91 16 93
-93 4 92 17 94
-94 5 93 18 95
-95 6 94 19 96
-96 7 95 20 97
-97 8 96 21 98
-98 22 99 9 97
-99 23 100 10 98
-100 11 99 24 101
-101 12 100 25 102
-102 13 101 26 103
-103 14 102 27 104
-104 15 103 28 105
-105 16 104 29 106
-106 17 105 30 107
-107 18 106 31 108
-108 19 107 32 109
-109 33 110 20 108
-110 34 111 21 109
-111 22 110 35 112
-112 23 111 36 113
-113 24 112 37 114
-114 25 113 38 115
-115 26 114 39 116
-116 27 115 40 117
-117 28 116 41 118
-118 29 117 42 119
-119 30 118 43 120
-120 44 121 31 119
-121 45 122 32 120
-122 33 121 46 123
-123 34 122 47 124
-124 35 123 48 125
-125 36 124 49 126
-126 37 125 50 127
-127 38 126 51 128
-128 39 127 52 129
-129 40 128 53 130
-130 41 129 54 131
-131 55 132 42 130
-132 56 133 43 131
-133 44 132 57 134
-134 45 133 58 135
-135 46 134 59 136
-136 47 135 60 137
-137 48 136 61 138
-138 49 137 62 139
-139 50 138 63 140
-140 51 139 64 141
-141 52 140 65 142
-142 66 143 53 141
-143 67 144 54 142
-144 55 143 68 145
-145 56 144 69 146
-146 57 145 70 147
-147 58 146 71 148
-148 59 147 72 149
-149 60 148 73 150
-150 61 149 74 151
-151 62 150 75 152
-152 63 151 76 153
-153 77 154 64 152
-154 78 155 65 153
-155 66 154 79 156
-156 67 155 80 157
-157 68 156 81 158
-158 69 157 82 159
-159 70 158 83 160
-160 71 159 84 161
-161 72 160 85 162
-162 73 161 86 163
-163 74 162 87 164
-164 88 165 75 163
-165 1 89 76 164
0