Graph forms
for C4 [ 192, 37 ] =
PL(MC3(6,16,1,9,7,0,1),[4^24,6^16])
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On this page are computer-accessible forms for the graph C4[ 192, 37 ] =
PL(MC3(6,16,1,9,7,0,1),[4^24,6^16]).
(I) Following is a form readable by MAGMA:
g:=Graph<192|{ {96, 103}, {96, 119}, {72, 104}, {69, 100}, {93, 124}, {91, 122},
{76, 110}, {89, 123}, {87, 116}, {85, 113}, {95, 123}, {88, 125}, {74, 109},
{82, 117}, {84, 124}, {94, 116}, {66, 105}, {92, 119}, {73, 98}, {79, 100}, {81,
122}, {73, 101}, {90, 118}, {77, 99}, {80, 127}, {69, 117}, {91, 107}, {76,
125}, {87, 102}, {74, 120}, {93, 111}, {67, 112}, {95, 108}, {86, 101}, {86,
98}, {89, 108}, {88, 110}, {66, 117}, {94, 102}, {72, 113}, {79, 118}, {81,
107}, {82, 105}, {92, 103}, {84, 111}, {67, 126}, {85, 104}, {90, 100}, {77,
114}, {42, 106}, {58, 120}, {51, 112}, {53, 118}, {35, 103}, {50, 117}, {62,
121}, {33, 105}, {32, 107}, {49, 122}, {39, 107}, {54, 122}, {52, 121}, {46,
97}, {61, 114}, {42, 121}, {45, 126}, {62, 106}, {50, 100}, {33, 118}, {35,
116}, {58, 109}, {52, 109}, {37, 127}, {54, 108}, {32, 123}, {34, 126}, {39,
123}, {53, 105}, {45, 112}, {49, 108}, {46, 115}, {61, 99}, {3, 99}, {9, 104},
{18, 115}, {14, 111}, {21, 119}, {10, 110}, {31, 121}, {4, 99}, {16, 119}, {2,
106}, {28, 116}, {7, 110}, {25, 115}, {1, 106}, {8, 101}, {29, 112}, {15, 98},
{6, 104}, {19, 125}, {15, 97}, {17, 126}, {3, 113}, {31, 109}, {14, 125}, {21,
102}, {6, 114}, {4, 113}, {10, 124}, {16, 102}, {18, 101}, {25, 97}, {1, 120},
{2, 120}, {5, 127}, {7, 124}, {28, 103}, {9, 114}, {8, 115}, {19, 111}, {30,
98}, {1, 127}, {30, 97}, {12, 140}, {40, 168}, {16, 144}, {13, 140}, {41, 168},
{24, 153}, {60, 189}, {65, 192}, {7, 133}, {22, 148}, {54, 180}, {58, 184}, {28,
159}, {61, 190}, {23, 147}, {48, 180}, {17, 148}, {43, 174}, {51, 181}, {14,
137}, {26, 157}, {59, 188}, {29, 149}, {38, 174}, {53, 189}, {72, 192}, {41,
160}, {44, 165}, {34, 168}, {6, 141}, {45, 166}, {41, 162}, {27, 151}, {39,
171}, {63, 179}, {28, 145}, {56, 181}, {61, 176}, {16, 158}, {55, 185}, {3,
140}, {42, 165}, {7, 151}, {41, 185}, {39, 183}, {55, 167}, {58, 170}, {12,
157}, {43, 186}, {35, 178}, {22, 135}, {17, 128}, {60, 173}, {1, 147}, {52,
166}, {31, 139}, {44, 184}, {51, 167}, {29, 136}, {36, 177}, {63, 170}, {5,
147}, {17, 135}, {59, 173}, {13, 154}, {26, 141}, {22, 129}, {14, 153}, {52,
163}, {53, 173}, {3, 154}, {42, 179}, {11, 146}, {8, 146}, {30, 132}, {57, 163},
{6, 157}, {48, 171}, {45, 182}, {34, 185}, {23, 139}, {56, 164}, {24, 133}, {47,
178}, {40, 181}, {38, 187}, {35, 190}, {31, 130}, {27, 133}, {29, 131}, {30,
129}, {54, 169}, {56, 167}, {57, 166}, {19, 179}, {48, 144}, {36, 132}, {37,
132}, {63, 158}, {26, 184}, {46, 140}, {43, 137}, {34, 128}, {2, 161}, {25,
186}, {24, 187}, {18, 177}, {57, 154}, {59, 152}, {37, 129}, {38, 130}, {21,
176}, {27, 190}, {23, 177}, {47, 137}, {9, 174}, {49, 150}, {40, 143}, {37,
130}, {62, 153}, {4, 172}, {23, 191}, {13, 165}, {8, 160}, {5, 172}, {50, 155},
{22, 191}, {60, 149}, {32, 138}, {56, 146}, {11, 160}, {27, 176}, {15, 164},
{36, 136}, {55, 155}, {11, 166}, {38, 139}, {18, 191}, {15, 162}, {12, 161},
{33, 143}, {48, 158}, {63, 145}, {10, 165}, {20, 164}, {26, 170}, {51, 131},
{36, 149}, {59, 138}, {10, 184}, {9, 186}, {46, 157}, {44, 159}, {2, 182}, {40,
156}, {24, 172}, {57, 141}, {20, 161}, {25, 172}, {20, 162}, {47, 153}, {20,
163}, {49, 134}, {32, 152}, {19, 170}, {55, 142}, {12, 182}, {60, 135}, {62,
133}, {43, 151}, {50, 142}, {44, 144}, {11, 182}, {33, 156}, {13, 179}, {4,
187}, {5, 186}, {64, 128}, {70, 134}, {64, 131}, {66, 129}, {74, 137}, {75,
143}, {85, 145}, {93, 152}, {94, 155}, {67, 139}, {90, 146}, {78, 134}, {65,
138}, {95, 148}, {85, 158}, {79, 132}, {86, 154}, {88, 150}, {91, 149}, {71,
136}, {83, 156}, {67, 147}, {70, 150}, {75, 155}, {80, 128}, {94, 143}, {77,
159}, {88, 138}, {80, 130}, {71, 148}, {80, 131}, {21, 192}, {68, 145}, {78,
152}, {65, 150}, {95, 136}, {68, 159}, {93, 134}, {86, 141}, {91, 135}, {74,
151}, {77, 144}, {83, 142}, {75, 171}, {89, 185}, {64, 161}, {92, 189}, {64,
163}, {84, 183}, {81, 181}, {73, 174}, {76, 171}, {83, 180}, {71, 175}, {70,
175}, {69, 175}, {87, 188}, {68, 169}, {96, 142}, {47, 192}, {78, 190}, {82,
162}, {65, 176}, {73, 187}, {82, 160}, {68, 183}, {92, 175}, {76, 180}, {69,
188}, {81, 168}, {72, 178}, {87, 173}, {83, 169}, {70, 189}, {71, 188}, {75,
183}, {96, 156}, {78, 178}, {66, 191}, {84, 169}, {79, 177}, {90, 164}, {89,
167} }>;
(II) A more general form is to represent the graph as the orbit of {96, 103}
under the group generated by the following permutations:
a: (16, 28)(21, 35)(32, 49)(39, 54)(48, 68)(59, 70)(65, 78)(75, 83)(76, 84)(87,
92)(88, 93)(94, 96)(102, 103)(107, 122)(108, 123)(110, 124)(111, 125)(116,
119)(134, 138)(142, 155)(143, 156)(144, 159)(145, 158)(150, 152)(169, 171)(173,
189)(175, 188)(176, 190)(178, 192)(180, 183) (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: (33, 50)(40, 55)(53, 69)(60, 71)(81, 89)(91, 95)(100, 118)(105, 117)(107,
123)(108, 122)(135, 148)(136, 149)(142, 156)(143, 155)(167, 181)(168, 185)(173,
188)(175, 189)
c: (7, 14)(10, 19)(27, 47)(44, 63)(61, 72)(77, 85)(99, 113)(104, 114)(110,
125)(111, 124)(133, 153)(137, 151)(144, 158)(145, 159)(165, 179)(170, 184)(176,
192)(178, 190)
d: (2, 5)(3, 8)(4, 11)(6, 15)(7, 29)(9, 20)(10, 36)(12, 25)(13, 18)(14, 17)(16,
50, 28, 33)(19, 22)(21, 55, 35, 40)(23, 42)(24, 45)(26, 30)(27, 51)(32, 49)(34,
47)(37, 58)(38, 52)(39, 70)(41, 72)(43, 64)(44, 79)(48, 69, 68, 53)(54, 59)(56,
61)(57, 73)(60, 76, 71, 84)(62, 67)(63, 66)(65, 89, 78, 81)(74, 80)(75, 92)(77,
90)(82, 85)(83, 87)(88, 95, 93, 91)(94, 96)(97, 157)(98, 141)(99, 146)(100, 159,
118, 144)(101, 154)(102, 142, 116, 156)(103, 143, 119, 155)(104, 162)(105, 158,
117, 145)(106, 147)(107, 150, 123, 134)(108, 152, 122, 138)(109, 130)(110, 136,
124, 149)(111, 135, 125, 148)(112, 133)(113, 160)(114, 164)(115, 140)(120,
127)(121, 139)(126, 153)(128, 137)(129, 170)(131, 151)(132, 184)(161, 186)(163,
174)(165, 177)(166, 187)(167, 190, 181, 176)(168, 192, 185, 178)(169, 173, 180,
188)(171, 175, 183, 189)(172, 182)(179, 191)
e: (8, 15)(11, 20)(17, 29)(18, 30)(22, 36)(23, 37)(34, 51)(41, 56)(45, 64)(66,
79)(67, 80)(82, 90)(97, 115)(98, 101)(100, 117)(105, 118)(112, 128)(126,
131)(127, 147)(129, 177)(130, 139)(132, 191)(135, 149)(136, 148)(146, 162)(160,
164)(161, 182)(163, 166)(167, 185)(168, 181)
f: (1, 2)(3, 4)(5, 12)(6, 9)(7, 10)(8, 30)(11, 37)(13, 24)(14, 19)(15, 18)(16,
21)(17, 51)(20, 23)(22, 56)(25, 46)(26, 43)(27, 44)(28, 35)(29, 34)(31, 52)(32,
39)(33, 53)(36, 41)(38, 57)(40, 60)(42, 62)(45, 80)(47, 63)(48, 65)(49, 54)(50,
69)(55, 71)(58, 74)(59, 75)(61, 77)(64, 67)(66, 90)(68, 78)(70, 83)(72, 85)(73,
86)(76, 88)(79, 82)(81, 91)(84, 93)(87, 94)(89, 95)(92, 96)(97, 115)(98,
101)(100, 117)(105, 118)(112, 128)(126, 131)(127, 182)(129, 146)(130, 166)(132,
160)(133, 165)(134, 169)(135, 181)(136, 185)(137, 170)(138, 171)(139, 163)(140,
172)(141, 174)(142, 175)(143, 173)(144, 176)(145, 178)(147, 161)(148, 167)(149,
168)(150, 180)(151, 184)(152, 183)(153, 179)(154, 187)(155, 188)(156, 189)(157,
186)(158, 192)(159, 190)(162, 177)(164, 191)
g: (17, 29)(22, 36)(34, 51)(41, 56)(66, 79)(82, 90)(100, 117)(105, 118)(112,
126)(128, 131)(129, 132)(135, 149)(136, 148)(146, 160)(162, 164)(167, 185)(168,
181)(177, 191)
h: (3, 6)(4, 9)(7, 14)(10, 19)(13, 26)(24, 43)(27, 47)(42, 58)(44, 63)(61,
72)(62, 74)(77, 85)(99, 104)(106, 120)(109, 121)(110, 125)(111, 124)(113,
114)(133, 137)(140, 157)(141, 154)(144, 158)(145, 159)(151, 153)(165, 170)(172,
186)(174, 187)(176, 192)(178, 190)(179, 184)
m: (1, 3)(2, 13)(4, 5)(6, 31)(7, 15, 14, 8)(9, 38)(10, 20, 19, 11)(12, 42)(16,
17, 28, 29)(18, 27, 30, 47)(21, 22, 35, 36)(23, 61, 37, 72)(24, 25)(26, 52)(32,
33)(34, 68, 51, 48)(39, 40)(41, 84, 56, 76)(43, 73)(44, 64, 63, 45)(46, 62)(49,
50)(53, 59)(54, 55)(57, 58)(60, 87)(65, 66, 78, 79)(67, 77, 80, 85)(69, 70)(71,
92)(74, 86)(75, 81)(82, 93, 90, 88)(83, 89)(91, 94)(95, 96)(97, 153, 115,
133)(98, 137, 101, 151)(99, 127, 113, 147)(100, 150, 117, 134)(102, 135, 116,
149)(103, 136, 119, 148)(104, 139, 114, 130)(105, 152, 118, 138)(106, 140)(107,
143)(108, 142)(109, 141)(110, 162, 111, 146)(112, 144, 128, 145)(120, 154)(121,
157)(122, 155)(123, 156)(124, 164, 125, 160)(126, 159, 131, 158)(129, 178, 177,
176)(132, 192, 191, 190)(161, 179, 182, 165)(163, 170, 166, 184)(167, 180, 185,
169)(168, 183, 181, 171)(186, 187)(188, 189)
C4[ 192, 37 ]
192
-1 147 127 106 120
-2 182 106 161 120
-3 99 154 113 140
-4 99 187 113 172
-5 147 127 172 186
-6 157 114 104 141
-7 110 133 124 151
-8 101 146 115 160
-9 114 104 174 186
-10 110 165 124 184
-11 166 146 160 182
-12 157 182 161 140
-13 154 165 179 140
-14 111 125 137 153
-15 162 97 98 164
-16 144 102 158 119
-17 135 126 148 128
-18 177 101 191 115
-19 111 179 125 170
-20 161 162 163 164
-21 176 102 192 119
-22 135 191 148 129
-23 177 147 191 139
-24 187 133 172 153
-25 115 172 97 186
-26 157 170 184 141
-27 176 133 190 151
-28 145 103 159 116
-29 112 136 149 131
-30 132 129 97 98
-31 121 139 130 109
-32 123 138 107 152
-33 143 156 105 118
-34 168 126 128 185
-35 178 190 103 116
-36 132 177 136 149
-37 132 127 129 130
-38 187 139 130 174
-39 123 171 183 107
-40 143 156 168 181
-41 168 160 162 185
-42 121 165 179 106
-43 137 151 174 186
-44 165 144 159 184
-45 166 112 126 182
-46 157 115 140 97
-47 178 137 192 153
-48 144 158 180 171
-49 122 134 150 108
-50 100 155 117 142
-51 112 167 181 131
-52 121 166 163 109
-53 189 105 118 173
-54 122 169 180 108
-55 155 167 185 142
-56 167 146 181 164
-57 154 166 141 163
-58 170 184 109 120
-59 188 138 173 152
-60 189 135 149 173
-61 99 176 190 114
-62 121 133 106 153
-63 145 179 158 170
-64 128 161 163 131
-65 176 192 138 150
-66 191 105 117 129
-67 112 147 126 139
-68 145 169 159 183
-69 100 188 117 175
-70 134 189 150 175
-71 188 136 148 175
-72 178 113 104 192
-73 187 101 174 98
-74 137 151 109 120
-75 143 155 171 183
-76 110 125 180 171
-77 99 144 114 159
-78 134 178 190 152
-79 132 100 177 118
-80 127 128 130 131
-81 122 168 181 107
-82 105 160 117 162
-83 156 169 180 142
-84 111 124 169 183
-85 145 113 158 104
-86 154 101 141 98
-87 188 102 116 173
-88 110 125 138 150
-89 123 167 108 185
-90 100 146 118 164
-91 122 135 149 107
-92 189 103 119 175
-93 111 134 124 152
-94 143 155 102 116
-95 123 136 148 108
-96 156 103 119 142
-97 46 25 15 30
-98 15 73 30 86
-99 77 3 4 61
-100 79 90 69 50
-101 18 73 8 86
-102 16 94 21 87
-103 35 92 28 96
-104 6 72 85 9
-105 33 66 82 53
-106 1 2 62 42
-107 91 81 39 32
-108 89 49 95 54
-109 58 52 74 31
-110 88 7 10 76
-111 14 93 84 19
-112 45 67 29 51
-113 3 4 72 85
-114 77 6 61 9
-115 46 25 18 8
-116 35 28 94 87
-117 66 69 82 50
-118 33 79 90 53
-119 92 16 96 21
-120 1 2 58 74
-121 62 52 31 42
-122 91 81 49 54
-123 89 39 95 32
-124 93 7 84 10
-125 88 14 19 76
-126 34 45 67 17
-127 1 80 37 5
-128 34 80 17 64
-129 22 66 37 30
-130 80 37 38 31
-131 80 29 51 64
-132 79 36 37 30
-133 24 27 7 62
-134 78 70 49 93
-135 22 91 60 17
-136 36 71 29 95
-137 14 47 74 43
-138 88 59 32 65
-139 23 67 38 31
-140 12 13 46 3
-141 57 26 6 86
-142 55 50 83 96
-143 33 94 40 75
-144 44 77 48 16
-145 68 28 63 85
-146 11 56 90 8
-147 1 23 67 5
-148 22 71 17 95
-149 36 91 60 29
-150 88 70 49 65
-151 27 7 74 43
-152 78 59 93 32
-153 24 14 47 62
-154 13 57 3 86
-155 55 50 94 75
-156 33 83 40 96
-157 12 46 26 6
-158 48 16 63 85
-159 44 77 68 28
-160 11 82 8 41
-161 12 2 20 64
-162 15 82 41 20
-163 57 52 20 64
-164 56 90 15 20
-165 44 13 42 10
-166 11 45 57 52
-167 55 56 89 51
-168 34 81 40 41
-169 68 83 84 54
-170 58 26 19 63
-171 48 39 75 76
-172 24 25 4 5
-173 59 60 53 87
-174 38 73 9 43
-175 69 70 92 71
-176 27 61 21 65
-177 23 79 36 18
-178 78 35 47 72
-179 13 19 63 42
-180 48 83 54 76
-181 56 81 40 51
-182 11 12 45 2
-183 68 39 84 75
-184 44 58 26 10
-185 55 34 89 41
-186 25 5 9 43
-187 24 4 38 73
-188 69 59 71 87
-189 70 92 60 53
-190 78 35 27 61
-191 22 66 23 18
-192 47 72 21 65
0