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