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