Graph forms
for C4 [ 192, 42 ] =
PL(LoPr_24(3,8,6,8,3),[6^16,8^12])
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On this page are computer-accessible forms for the graph C4[ 192, 42 ] =
PL(LoPr_24(3,8,6,8,3),[6^16,8^12]).
(I) Following is a form readable by MAGMA:
g:=Graph<192|{ {96, 116}, {96, 122}, {66, 99}, {91, 122}, {78, 108}, {87, 117},
{84, 119}, {87, 115}, {90, 126}, {70, 99}, {95, 122}, {90, 124}, {65, 102}, {73,
110}, {84, 115}, {85, 114}, {69, 109}, {70, 110}, {75, 98}, {93, 116}, {82,
123}, {86, 122}, {68, 105}, {95, 114}, {64, 110}, {81, 126}, {83, 124}, {92,
108}, {94, 110}, {93, 109}, {65, 112}, {80, 98}, {64, 115}, {86, 101}, {66,
117}, {92, 101}, {73, 115}, {69, 126}, {89, 98}, {78, 117}, {89, 101}, {68,
121}, {91, 101}, {75, 116}, {44, 108}, {57, 121}, {35, 98}, {37, 100}, {51,
112}, {49, 117}, {58, 126}, {63, 123}, {33, 100}, {43, 109}, {46, 105}, {53,
114}, {60, 123}, {46, 102}, {56, 112}, {52, 125}, {62, 119}, {61, 119}, {39,
106}, {36, 106}, {43, 100}, {57, 105}, {49, 99}, {52, 103}, {39, 113}, {35,
116}, {58, 109}, {59, 99}, {37, 124}, {53, 108}, {33, 123}, {44, 114}, {56,
102}, {16, 113}, {10, 104}, {5, 102}, {30, 125}, {13, 105}, {2, 103}, {28, 121},
{24, 125}, {14, 107}, {4, 97}, {6, 97}, {12, 107}, {31, 119}, {6, 111}, {4,
111}, {23, 124}, {19, 120}, {7, 107}, {29, 113}, {28, 112}, {13, 97}, {2, 111},
{18, 127}, {1, 111}, {7, 104}, {25, 118}, {22, 103}, {25, 104}, {23, 100}, {9,
125}, {12, 120}, {11, 127}, {3, 118}, {20, 97}, {29, 106}, {1, 121}, {19, 107},
{9, 113}, {30, 103}, {3, 120}, {10, 118}, {22, 106}, {2, 127}, {21, 104}, {5,
120}, {1, 127}, {8, 118}, {1, 129}, {8, 136}, {5, 132}, {18, 147}, {59, 186},
{16, 146}, {39, 165}, {35, 161}, {27, 153}, {26, 152}, {15, 140}, {42, 169},
{41, 170}, {52, 183}, {56, 187}, {8, 140}, {48, 180}, {36, 160}, {14, 138}, {9,
141}, {15, 137}, {40, 174}, {32, 166}, {3, 132}, {21, 146}, {55, 176}, {45,
165}, {59, 179}, {23, 158}, {63, 182}, {62, 180}, {63, 181}, {3, 136}, {31,
148}, {24, 147}, {22, 157}, {21, 158}, {16, 155}, {57, 178}, {20, 152}, {47,
163}, {17, 156}, {44, 161}, {27, 150}, {9, 135}, {38, 168}, {21, 155}, {55,
185}, {78, 192}, {26, 149}, {47, 160}, {31, 143}, {38, 182}, {27, 138}, {13,
159}, {42, 184}, {40, 186}, {23, 133}, {26, 137}, {45, 190}, {57, 170}, {33,
181}, {43, 191}, {32, 181}, {43, 189}, {14, 153}, {20, 131}, {56, 175}, {8,
144}, {11, 147}, {59, 163}, {62, 166}, {5, 156}, {39, 190}, {27, 130}, {26,
131}, {7, 158}, {62, 167}, {15, 149}, {63, 165}, {17, 138}, {41, 178}, {31,
132}, {28, 128}, {92, 192}, {33, 189}, {16, 141}, {48, 173}, {28, 129}, {24,
134}, {60, 162}, {2, 157}, {24, 135}, {15, 144}, {52, 171}, {34, 130}, {53,
149}, {18, 179}, {54, 151}, {18, 177}, {40, 139}, {30, 186}, {34, 134}, {6,
163}, {50, 151}, {37, 128}, {35, 134}, {7, 162}, {47, 137}, {50, 148}, {48,
151}, {51, 148}, {61, 154}, {45, 133}, {12, 166}, {44, 134}, {4, 175}, {38,
141}, {13, 161}, {49, 157}, {29, 177}, {19, 191}, {17, 189}, {14, 162}, {54,
154}, {58, 150}, {10, 167}, {41, 132}, {60, 145}, {29, 179}, {55, 153}, {25,
182}, {36, 139}, {30, 174}, {32, 144}, {25, 168}, {46, 159}, {42, 155}, {34,
147}, {61, 140}, {11, 185}, {49, 131}, {46, 156}, {60, 142}, {61, 143}, {38,
149}, {45, 158}, {51, 128}, {54, 133}, {34, 150}, {20, 161}, {17, 167}, {22,
160}, {10, 189}, {50, 133}, {19, 164}, {55, 128}, {48, 136}, {53, 141}, {12,
181}, {40, 146}, {42, 144}, {11, 176}, {32, 155}, {58, 129}, {37, 153}, {50,
142}, {41, 148}, {51, 142}, {54, 139}, {36, 154}, {4, 187}, {82, 146}, {73,
136}, {75, 138}, {67, 129}, {83, 145}, {82, 145}, {91, 152}, {6, 192}, {64,
137}, {86, 159}, {74, 131}, {77, 135}, {69, 142}, {96, 171}, {66, 140}, {76,
130}, {94, 145}, {96, 176}, {94, 143}, {76, 159}, {86, 130}, {67, 150}, {77,
152}, {74, 157}, {75, 156}, {66, 154}, {82, 139}, {83, 143}, {91, 135}, {73,
151}, {64, 160}, {94, 190}, {92, 188}, {71, 167}, {88, 185}, {80, 178}, {93,
191}, {89, 187}, {71, 164}, {79, 172}, {77, 169}, {85, 177}, {89, 188}, {72,
174}, {74, 172}, {69, 162}, {78, 169}, {67, 171}, {68, 172}, {76, 164}, {81,
185}, {80, 187}, {65, 173}, {79, 163}, {72, 165}, {93, 176}, {85, 184}, {95,
177}, {47, 192}, {88, 183}, {72, 184}, {90, 170}, {84, 166}, {71, 180}, {76,
191}, {67, 183}, {95, 171}, {88, 172}, {80, 164}, {65, 180}, {71, 178}, {77,
184}, {74, 188}, {88, 175}, {90, 173}, {68, 188}, {70, 190}, {79, 183}, {81,
170}, {85, 174}, {70, 186}, {79, 179}, {84, 168}, {72, 182}, {87, 169}, {81,
175}, {83, 173}, {87, 168} }>;
(II) A more general form is to represent the graph as the orbit of {96, 116}
under the group generated by the following permutations:
a: (1, 3, 22, 46, 54, 20, 51, 15)(2, 5, 36, 13, 50, 26, 28, 8)(4, 31, 47, 57,
73, 74, 65, 66)(6, 41, 64, 68, 48, 49, 56, 61)(7, 9, 27, 21, 24, 14, 16, 34)(10,
30, 75, 82, 44, 69, 38, 67)(11, 12, 29, 76, 45, 91, 37, 42)(17, 40, 35, 60, 53,
58, 25, 52)(18, 19, 39, 86, 23, 77, 55, 32)(33, 85, 93, 63, 95, 43, 72, 96)(59,
80, 94, 92, 90, 87, 88, 62)(70, 89, 83, 78, 81, 84, 79, 71)(97, 148, 137, 121,
136, 157, 102, 154)(98, 145, 108, 126, 168, 183, 167, 186)(99, 187, 143, 192,
170, 115, 172, 180)(100, 184, 176, 181, 177, 191, 165, 122)(101, 124, 169, 185,
166, 179, 164, 190)(103, 156, 139, 161, 142, 149, 129, 118)(104, 125, 138, 146,
134, 162, 141, 150)(105, 151, 131, 112, 140, 111, 132, 160)(106, 159, 133, 152,
128, 144, 127, 120)(107, 113, 130, 158, 135, 153, 155, 147)(109, 182, 171, 189,
174, 116, 123, 114)(110, 188, 173, 117, 175, 119, 163, 178) (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, 22, 36, 54, 50, 51, 28)(3, 14, 46, 34, 20, 9, 15, 21)(4, 52, 47, 40,
73, 60, 65, 58)(5, 27, 13, 24, 26, 16, 8, 7)(6, 30, 64, 82, 48, 69, 56, 67)(10,
19, 75, 86, 44, 77, 38, 32)(11, 74, 29, 66, 45, 31, 37, 57)(12, 17, 76, 35, 91,
53, 42, 25)(18, 49, 39, 61, 23, 41, 55, 68)(33, 71, 93, 89, 95, 78, 72, 84)(43,
80, 96, 92, 85, 87, 63, 62)(59, 70, 94, 83, 90, 81, 88, 79)(97, 125, 137, 146,
136, 162, 102, 150)(98, 122, 108, 184, 168, 181, 167, 191)(99, 190, 143, 124,
170, 185, 172, 179)(100, 178, 176, 188, 177, 117, 165, 119)(101, 114, 169, 182,
166, 189, 164, 116)(103, 160, 139, 151, 142, 112, 129, 111)(104, 120, 138, 159,
134, 152, 141, 144)(105, 147, 131, 113, 140, 158, 132, 153)(106, 154, 133, 148,
128, 121, 127, 157)(107, 156, 130, 161, 135, 149, 155, 118)(109, 187, 171, 192,
174, 115, 123, 180)(110, 145, 173, 126, 175, 183, 163, 186)
c: (2, 28)(3, 16)(4, 67)(5, 9)(6, 58)(7, 15)(8, 21)(10, 42)(11, 68)(12, 38)(13,
34)(14, 26)(17, 77)(18, 57)(19, 53)(20, 27)(22, 51)(23, 66)(24, 46)(25, 32)(29,
41)(30, 65)(31, 39)(33, 87)(35, 86)(36, 50)(37, 49)(40, 48)(43, 78)(44, 76)(45,
61)(47, 69)(52, 56)(55, 74)(59, 90)(60, 64)(62, 72)(63, 84)(70, 83)(71, 85)(73,
82)(75, 91)(79, 81)(80, 95)(89, 96)(92, 93)(97, 150)(98, 122)(99, 124)(100,
117)(101, 116)(102, 125)(103, 112)(104, 144)(105, 147)(106, 148)(107, 149)(108,
191)(109, 192)(110, 145)(111, 129)(113, 132)(114, 164)(115, 123)(118, 155)(119,
165)(120, 141)(121, 127)(126, 163)(128, 157)(130, 161)(131, 153)(133, 154)(134,
159)(135, 156)(136, 146)(137, 162)(138, 152)(139, 151)(140, 158)(142, 160)(143,
190)(166, 182)(167, 184)(168, 181)(169, 189)(170, 179)(171, 187)(172, 185)(173,
186)(174, 180)(175, 183)(176, 188)(177, 178)
d: (3, 7)(4, 11)(5, 14)(6, 18)(8, 21)(9, 26)(13, 34)(15, 16)(20, 24)(23, 48)(27,
46)(29, 47)(30, 49)(31, 60)(33, 62)(37, 65)(39, 64)(40, 66)(41, 69)(43, 71)(45,
73)(52, 74)(55, 56)(57, 58)(61, 82)(63, 84)(67, 68)(72, 87)(78, 85)(80, 93)(89,
96)(92, 95)(97, 147)(98, 116)(99, 186)(100, 180)(101, 122)(102, 153)(103,
157)(104, 118)(105, 150)(106, 160)(107, 120)(108, 114)(109, 178)(110, 190)(111,
127)(112, 128)(113, 137)(115, 165)(117, 174)(119, 123)(121, 129)(124, 173)(125,
131)(126, 170)(130, 159)(132, 162)(133, 151)(134, 161)(135, 152)(136, 158)(138,
156)(139, 154)(140, 146)(141, 149)(142, 148)(143, 145)(144, 155)(163, 179)(164,
191)(166, 181)(167, 189)(168, 182)(169, 184)(171, 188)(172, 183)(175, 185)(176,
187)(177, 192)
e: (1, 4, 89, 86, 34, 11, 88, 68, 13, 35, 96, 67)(2, 56, 92, 76, 24, 55, 79, 57,
20, 75, 95, 58)(3, 38, 33, 40, 50, 64, 62, 42, 7, 39, 83, 66)(5, 53, 43, 30, 51,
47, 71, 77, 14, 29, 90, 49)(6, 80, 91, 27, 18, 81, 74, 46, 44, 93, 52, 28)(8,
25, 63, 82, 54, 73, 84, 32, 21, 45, 94, 61)(9, 37, 59, 41, 26, 17, 85, 69, 22,
65, 78, 19)(10, 72, 60, 36, 48, 87, 12, 16, 23, 70, 31, 15)(97, 98, 122, 150,
127, 175, 188, 159, 134, 176, 183, 121)(99, 132, 149, 189, 174, 142, 160, 180,
169, 107, 113, 124)(100, 186, 148, 137, 167, 184, 162, 106, 173, 117, 120,
141)(101, 130, 147, 185, 172, 105, 161, 116, 171, 129, 111, 187)(102, 108, 191,
125, 128, 163, 178, 152, 138, 177, 126, 157)(103, 112, 192, 164, 135, 153, 179,
170, 131, 156, 114, 109)(104, 165, 145, 154, 136, 168, 181, 146, 133, 110, 119,
144)(115, 166, 155, 158, 190, 143, 140, 118, 182, 123, 139, 151)
C4[ 192, 42 ]
192
-1 121 111 127 129
-2 111 157 103 127
-3 132 136 118 120
-4 187 111 97 175
-5 132 156 102 120
-6 111 192 97 163
-7 158 104 107 162
-8 144 136 118 140
-9 113 135 125 141
-10 167 189 104 118
-11 176 147 127 185
-12 166 181 107 120
-13 159 105 161 97
-14 138 107 162 153
-15 144 137 149 140
-16 155 113 146 141
-17 156 167 189 138
-18 177 179 147 127
-19 191 107 120 164
-20 161 97 152 131
-21 155 146 158 104
-22 157 103 160 106
-23 100 133 124 158
-24 134 135 125 147
-25 168 104 182 118
-26 137 149 152 131
-27 138 150 130 153
-28 121 112 128 129
-29 177 113 179 106
-30 103 125 174 186
-31 132 143 148 119
-32 144 155 166 181
-33 100 123 189 181
-34 134 147 150 130
-35 134 116 161 98
-36 154 160 106 139
-37 100 124 128 153
-38 168 149 182 141
-39 165 113 190 106
-40 146 139 174 186
-41 132 178 148 170
-42 144 155 169 184
-43 100 189 191 109
-44 134 114 161 108
-45 165 133 190 158
-46 156 102 159 105
-47 137 192 160 163
-48 136 180 151 173
-49 99 157 117 131
-50 133 148 151 142
-51 112 148 128 142
-52 103 125 171 183
-53 114 149 108 141
-54 154 133 139 151
-55 176 128 185 153
-56 187 112 102 175
-57 121 178 170 105
-58 126 150 129 109
-59 99 179 163 186
-60 123 145 162 142
-61 143 154 140 119
-62 166 167 180 119
-63 165 123 181 182
-64 110 115 137 160
-65 112 102 180 173
-66 99 154 117 140
-67 171 150 183 129
-68 121 188 105 172
-69 126 162 109 142
-70 99 110 190 186
-71 167 178 180 164
-72 165 182 184 174
-73 110 136 115 151
-74 188 157 172 131
-75 156 116 138 98
-76 191 159 130 164
-77 135 169 184 152
-78 169 192 117 108
-79 179 172 183 163
-80 187 178 98 164
-81 126 170 185 175
-82 123 145 146 139
-83 143 145 124 173
-84 166 168 115 119
-85 177 114 184 174
-86 122 101 159 130
-87 168 169 115 117
-88 172 183 185 175
-89 187 188 101 98
-90 124 126 170 173
-91 122 101 135 152
-92 188 101 192 108
-93 176 191 116 109
-94 110 143 145 190
-95 122 177 114 171
-96 176 122 116 171
-97 13 4 6 20
-98 89 35 80 75
-99 66 59 70 49
-100 33 23 37 43
-101 89 91 92 86
-102 56 46 5 65
-103 22 2 30 52
-104 25 7 10 21
-105 68 57 46 13
-106 22 36 39 29
-107 12 14 7 19
-108 44 78 92 53
-109 58 69 93 43
-110 70 94 73 64
-111 1 2 4 6
-112 56 28 51 65
-113 16 39 29 9
-114 44 95 85 53
-115 73 84 64 87
-116 35 93 96 75
-117 66 78 49 87
-118 3 25 8 10
-119 61 62 84 31
-120 12 3 5 19
-121 1 57 68 28
-122 91 95 96 86
-123 33 60 82 63
-124 23 90 37 83
-125 24 30 52 9
-126 90 58 69 81
-127 11 1 2 18
-128 55 37 28 51
-129 1 67 58 28
-130 34 27 86 76
-131 26 49 74 20
-132 3 5 41 31
-133 23 45 50 54
-134 44 34 24 35
-135 77 24 91 9
-136 3 48 73 8
-137 47 15 26 64
-138 14 27 17 75
-139 36 82 40 54
-140 66 15 61 8
-141 16 38 9 53
-142 69 60 50 51
-143 61 83 94 31
-144 15 8 42 32
-145 60 82 83 94
-146 16 82 40 21
-147 11 34 24 18
-148 50 51 41 31
-149 15 26 38 53
-150 34 67 58 27
-151 48 50 73 54
-152 77 91 26 20
-153 55 14 37 27
-154 66 36 61 54
-155 16 42 21 32
-156 46 5 17 75
-157 22 2 49 74
-158 23 45 7 21
-159 13 46 86 76
-160 22 36 47 64
-161 44 13 35 20
-162 14 69 60 7
-163 79 47 59 6
-164 80 71 19 76
-165 45 39 72 63
-166 12 62 84 32
-167 71 17 62 10
-168 25 38 84 87
-169 77 78 42 87
-170 57 90 81 41
-171 67 95 52 96
-172 88 68 79 74
-173 90 48 83 65
-174 72 40 30 85
-175 88 56 4 81
-176 11 55 93 96
-177 18 29 95 85
-178 57 80 71 41
-179 79 59 18 29
-180 48 71 62 65
-181 33 12 63 32
-182 25 38 72 63
-183 88 67 79 52
-184 77 72 85 42
-185 11 55 88 81
-186 59 70 40 30
-187 56 89 80 4
-188 89 68 92 74
-189 33 17 10 43
-190 45 70 39 94
-191 93 19 43 76
-192 78 47 92 6
0