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