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