Graph forms
for C4 [ 198, 4 ] = PS(6,33;10)
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On this page are computer-accessible forms for the graph C4[ 198, 4 ] =
PS(6,33;10).
(I) Following is a form readable by MAGMA:
g:=Graph<198|{ {33, 34}, {165, 166}, {99, 100}, {64, 74}, {65, 75}, {128, 138},
{129, 139}, {132, 142}, {66, 76}, {130, 140}, {131, 141}, {64, 87}, {128, 151},
{65, 88}, {129, 152}, {131, 154}, {66, 89}, {130, 153}, {132, 155}, {2, 34},
{83, 115}, {82, 114}, {81, 113}, {80, 112}, {79, 111}, {78, 110}, {77, 109},
{76, 108}, {75, 107}, {74, 106}, {73, 105}, {72, 104}, {71, 103}, {70, 102},
{69, 101}, {68, 100}, {3, 35}, {4, 36}, {5, 37}, {6, 38}, {7, 39}, {8, 40}, {9,
41}, {10, 42}, {11, 43}, {12, 44}, {13, 45}, {14, 46}, {15, 47}, {16, 48}, {17,
49}, {18, 50}, {19, 51}, {20, 52}, {21, 53}, {22, 54}, {23, 55}, {24, 56}, {25,
57}, {26, 58}, {27, 59}, {28, 60}, {29, 61}, {30, 62}, {31, 63}, {84, 116}, {85,
117}, {86, 118}, {87, 119}, {88, 120}, {89, 121}, {90, 122}, {91, 123}, {92,
124}, {93, 125}, {94, 126}, {95, 127}, {134, 166}, {135, 167}, {136, 168}, {137,
169}, {138, 170}, {139, 171}, {140, 172}, {141, 173}, {142, 174}, {143, 175},
{144, 176}, {145, 177}, {146, 178}, {147, 179}, {148, 180}, {149, 181}, {150,
182}, {151, 183}, {152, 184}, {153, 185}, {154, 186}, {155, 187}, {156, 188},
{157, 189}, {158, 190}, {159, 191}, {1, 35}, {81, 115}, {80, 114}, {77, 111},
{76, 110}, {73, 107}, {72, 106}, {69, 103}, {68, 102}, {4, 38}, {5, 39}, {8,
42}, {9, 43}, {12, 46}, {13, 47}, {16, 50}, {17, 51}, {20, 54}, {21, 55}, {24,
58}, {25, 59}, {28, 62}, {29, 63}, {84, 118}, {85, 119}, {88, 122}, {89, 123},
{92, 126}, {93, 127}, {133, 167}, {136, 170}, {137, 171}, {140, 174}, {141,
175}, {144, 178}, {145, 179}, {148, 182}, {149, 183}, {152, 186}, {153, 187},
{156, 190}, {157, 191}, {2, 36}, {83, 117}, {82, 116}, {75, 109}, {74, 108},
{67, 101}, {3, 37}, {10, 44}, {11, 45}, {18, 52}, {19, 53}, {26, 60}, {27, 61},
{90, 124}, {91, 125}, {138, 172}, {139, 173}, {146, 180}, {147, 181}, {154,
188}, {155, 189}, {6, 40}, {71, 105}, {70, 104}, {7, 41}, {22, 56}, {23, 57},
{86, 120}, {87, 121}, {134, 168}, {135, 169}, {150, 184}, {151, 185}, {14, 48},
{79, 113}, {78, 112}, {15, 49}, {142, 176}, {143, 177}, {1, 66}, {133, 198},
{40, 96}, {43, 99}, {42, 98}, {41, 97}, {53, 96}, {55, 98}, {54, 97}, {56, 99},
{30, 64}, {31, 65}, {158, 192}, {159, 193}, {32, 64}, {165, 197}, {164, 196},
{33, 65}, {160, 192}, {161, 193}, {162, 194}, {163, 195}, {32, 66}, {164, 198},
{160, 194}, {161, 195}, {162, 196}, {163, 197}, {45, 68}, {63, 86}, {61, 84},
{59, 82}, {57, 80}, {47, 70}, {36, 79}, {62, 85}, {58, 81}, {52, 95}, {48, 91},
{46, 69}, {35, 78}, {51, 94}, {49, 92}, {34, 77}, {60, 83}, {50, 93}, {44, 67},
{37, 80}, {47, 90}, {45, 88}, {39, 82}, {62, 72}, {63, 73}, {38, 81}, {56, 79},
{48, 71}, {46, 89}, {34, 90}, {39, 95}, {38, 94}, {37, 93}, {36, 92}, {35, 91},
{49, 72}, {55, 78}, {53, 76}, {51, 74}, {57, 67}, {61, 71}, {60, 70}, {40, 83},
{54, 77}, {50, 73}, {44, 87}, {41, 84}, {43, 86}, {58, 68}, {59, 69}, {42, 85},
{52, 75}, {32, 174}, {33, 175}, {32, 187}, {33, 188}, {13, 168}, {15, 170}, {21,
176}, {23, 178}, {29, 184}, {31, 186}, {14, 169}, {22, 177}, {30, 185}, {12,
167}, {24, 179}, {28, 183}, {11, 166}, {25, 180}, {27, 182}, {16, 191}, {26,
181}, {1, 176}, {3, 178}, {5, 180}, {7, 182}, {9, 184}, {11, 186}, {13, 188},
{15, 190}, {26, 168}, {27, 169}, {30, 172}, {31, 173}, {2, 177}, {6, 181}, {10,
185}, {14, 189}, {28, 170}, {29, 171}, {4, 179}, {12, 187}, {16, 171}, {20,
175}, {1, 189}, {2, 190}, {3, 191}, {17, 172}, {19, 174}, {24, 166}, {25, 167},
{8, 183}, {18, 173}, {4, 192}, {5, 193}, {6, 194}, {7, 195}, {67, 132}, {104,
160}, {105, 161}, {106, 162}, {107, 163}, {108, 164}, {109, 165}, {8, 196}, {9,
197}, {10, 198}, {17, 192}, {19, 194}, {21, 196}, {23, 198}, {18, 193}, {22,
197}, {117, 160}, {119, 162}, {20, 195}, {118, 161}, {120, 163}, {121, 164},
{94, 128}, {95, 129}, {122, 165}, {96, 128}, {97, 129}, {98, 130}, {99, 131},
{96, 130}, {97, 131}, {98, 132}, {111, 134}, {121, 144}, {123, 146}, {125, 148},
{127, 150}, {100, 143}, {110, 133}, {112, 155}, {116, 159}, {122, 145}, {126,
149}, {113, 156}, {115, 158}, {114, 157}, {124, 147}, {101, 144}, {103, 146},
{109, 152}, {111, 154}, {126, 136}, {127, 137}, {102, 145}, {110, 153}, {112,
135}, {120, 143}, {100, 156}, {101, 157}, {102, 158}, {103, 159}, {113, 136},
{115, 138}, {117, 140}, {119, 142}, {124, 134}, {125, 135}, {104, 147}, {108,
151}, {114, 137}, {118, 141}, {105, 148}, {107, 150}, {123, 133}, {106, 149},
{116, 139} }>;
(II) A more general form is to represent the graph as the orbit of {33, 34}
under the group generated by the following permutations:
a: (2, 24)(3, 14)(5, 27)(6, 17)(8, 30)(9, 20)(11, 33)(12, 23)(15, 26)(18,
29)(21, 32)(34, 166)(35, 189)(36, 179)(37, 169)(38, 192)(39, 182)(40, 172)(41,
195)(42, 185)(43, 175)(44, 198)(45, 188)(46, 178)(47, 168)(48, 191)(49, 181)(50,
171)(51, 194)(52, 184)(53, 174)(54, 197)(55, 187)(56, 177)(57, 167)(58, 190)(59,
180)(60, 170)(61, 193)(62, 183)(63, 173)(64, 196)(65, 186)(66, 176)(67, 133)(68,
156)(69, 146)(70, 136)(71, 159)(72, 149)(73, 139)(74, 162)(75, 152)(76, 142)(77,
165)(78, 155)(79, 145)(80, 135)(81, 158)(82, 148)(83, 138)(84, 161)(85, 151)(86,
141)(87, 164)(88, 154)(89, 144)(90, 134)(91, 157)(92, 147)(93, 137)(94, 160)(95,
150)(96, 140)(97, 163)(98, 153)(99, 143)(101, 123)(102, 113)(104, 126)(105,
116)(107, 129)(108, 119)(110, 132)(111, 122)(114, 125)(117, 128)(120, 131) (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, 79)(3, 157)(5, 82)(6, 160)(8, 85)(9, 163)(11, 88)(12, 133)(14, 91)(15,
136)(17, 94)(18, 139)(20, 97)(21, 142)(23, 67)(24, 145)(26, 70)(27, 148)(29,
73)(30, 151)(32, 76)(33, 154)(34, 111)(35, 189)(37, 114)(38, 192)(40, 117)(41,
195)(43, 120)(44, 198)(46, 123)(47, 168)(49, 126)(50, 171)(52, 129)(53, 174)(55,
132)(56, 177)(58, 102)(59, 180)(61, 105)(62, 183)(64, 108)(65, 186)(69, 146)(72,
149)(75, 152)(78, 155)(81, 158)(84, 161)(87, 164)(90, 134)(93, 137)(96, 140)(99,
143)(101, 178)(104, 181)(107, 184)(110, 187)(113, 190)(116, 193)(119, 196)(122,
166)(125, 169)(128, 172)(131, 175)
c: (2, 11)(3, 21)(4, 31)(5, 8)(6, 18)(7, 28)(9, 15)(10, 25)(13, 22)(14, 32)(16,
19)(17, 29)(20, 26)(24, 33)(27, 30)(34, 166)(35, 176)(36, 186)(37, 196)(38,
173)(39, 183)(40, 193)(41, 170)(42, 180)(43, 190)(44, 167)(45, 177)(46, 187)(47,
197)(48, 174)(49, 184)(50, 194)(51, 171)(52, 181)(53, 191)(54, 168)(55, 178)(56,
188)(57, 198)(58, 175)(59, 185)(60, 195)(61, 172)(62, 182)(63, 192)(64, 169)(65,
179)(66, 189)(67, 133)(68, 143)(69, 153)(70, 163)(71, 140)(72, 150)(73, 160)(74,
137)(75, 147)(76, 157)(77, 134)(78, 144)(79, 154)(80, 164)(81, 141)(82, 151)(83,
161)(84, 138)(85, 148)(86, 158)(87, 135)(88, 145)(89, 155)(90, 165)(91, 142)(92,
152)(93, 162)(94, 139)(95, 149)(96, 159)(97, 136)(98, 146)(99, 156)(101,
110)(102, 120)(103, 130)(104, 107)(105, 117)(106, 127)(108, 114)(109, 124)(112,
121)(113, 131)(115, 118)(116, 128)(119, 125)(123, 132)(126, 129)
d: (1, 34)(2, 35)(3, 36)(4, 37)(5, 38)(6, 39)(7, 40)(8, 41)(9, 42)(10, 43)(11,
44)(12, 45)(13, 46)(14, 47)(15, 48)(16, 49)(17, 50)(18, 51)(19, 52)(20, 53)(21,
54)(22, 55)(23, 56)(24, 57)(25, 58)(26, 59)(27, 60)(28, 61)(29, 62)(30, 63)(31,
64)(32, 65)(33, 66)(67, 166)(68, 167)(69, 168)(70, 169)(71, 170)(72, 171)(73,
172)(74, 173)(75, 174)(76, 175)(77, 176)(78, 177)(79, 178)(80, 179)(81, 180)(82,
181)(83, 182)(84, 183)(85, 184)(86, 185)(87, 186)(88, 187)(89, 188)(90, 189)(91,
190)(92, 191)(93, 192)(94, 193)(95, 194)(96, 195)(97, 196)(98, 197)(99,
198)(100, 133)(101, 134)(102, 135)(103, 136)(104, 137)(105, 138)(106, 139)(107,
140)(108, 141)(109, 142)(110, 143)(111, 144)(112, 145)(113, 146)(114, 147)(115,
148)(116, 149)(117, 150)(118, 151)(119, 152)(120, 153)(121, 154)(122, 155)(123,
156)(124, 157)(125, 158)(126, 159)(127, 160)(128, 161)(129, 162)(130, 163)(131,
164)(132, 165)
e: (1, 2)(3, 33)(4, 32)(5, 31)(6, 30)(7, 29)(8, 28)(9, 27)(10, 26)(11, 25)(12,
24)(13, 23)(14, 22)(15, 21)(16, 20)(17, 19)(34, 35)(36, 66)(37, 65)(38, 64)(39,
63)(40, 62)(41, 61)(42, 60)(43, 59)(44, 58)(45, 57)(46, 56)(47, 55)(48, 54)(49,
53)(50, 52)(67, 68)(69, 99)(70, 98)(71, 97)(72, 96)(73, 95)(74, 94)(75, 93)(76,
92)(77, 91)(78, 90)(79, 89)(80, 88)(81, 87)(82, 86)(83, 85)(100, 101)(102,
132)(103, 131)(104, 130)(105, 129)(106, 128)(107, 127)(108, 126)(109, 125)(110,
124)(111, 123)(112, 122)(113, 121)(114, 120)(115, 119)(116, 118)(133, 134)(135,
165)(136, 164)(137, 163)(138, 162)(139, 161)(140, 160)(141, 159)(142, 158)(143,
157)(144, 156)(145, 155)(146, 154)(147, 153)(148, 152)(149, 151)(166, 167)(168,
198)(169, 197)(170, 196)(171, 195)(172, 194)(173, 193)(174, 192)(175, 191)(176,
190)(177, 189)(178, 188)(179, 187)(180, 186)(181, 185)(182, 184)
C4[ 198, 4 ]
198
-1 66 176 35 189
-2 34 177 36 190
-3 35 178 37 191
-4 36 179 38 192
-5 37 180 39 193
-6 38 181 40 194
-7 39 182 41 195
-8 40 183 42 196
-9 41 184 43 197
-10 44 198 42 185
-11 45 166 43 186
-12 44 187 46 167
-13 45 188 47 168
-14 46 189 48 169
-15 47 190 49 170
-16 48 191 50 171
-17 49 192 51 172
-18 50 193 52 173
-19 51 194 53 174
-20 52 195 54 175
-21 55 176 53 196
-22 56 177 54 197
-23 55 198 57 178
-24 56 166 58 179
-25 57 167 59 180
-26 58 168 60 181
-27 59 169 61 182
-28 60 170 62 183
-29 61 171 63 184
-30 62 172 64 185
-31 63 173 65 186
-32 66 187 64 174
-33 34 188 65 175
-34 33 77 2 90
-35 1 78 3 91
-36 2 79 4 92
-37 3 80 5 93
-38 4 81 6 94
-39 5 82 7 95
-40 6 83 8 96
-41 7 84 9 97
-42 8 85 10 98
-43 11 99 9 86
-44 12 67 10 87
-45 11 88 13 68
-46 12 89 14 69
-47 13 90 15 70
-48 14 91 16 71
-49 15 92 17 72
-50 16 93 18 73
-51 17 94 19 74
-52 18 95 20 75
-53 19 96 21 76
-54 22 77 20 97
-55 23 78 21 98
-56 22 99 24 79
-57 23 67 25 80
-58 24 68 26 81
-59 25 69 27 82
-60 26 70 28 83
-61 27 71 29 84
-62 28 72 30 85
-63 29 73 31 86
-64 30 74 32 87
-65 33 88 31 75
-66 1 89 32 76
-67 44 132 57 101
-68 45 100 58 102
-69 46 101 59 103
-70 47 102 60 104
-71 48 103 61 105
-72 49 104 62 106
-73 50 105 63 107
-74 51 106 64 108
-75 52 107 65 109
-76 66 110 53 108
-77 34 111 54 109
-78 55 110 35 112
-79 56 111 36 113
-80 57 112 37 114
-81 58 113 38 115
-82 59 114 39 116
-83 60 115 40 117
-84 61 116 41 118
-85 62 117 42 119
-86 63 118 43 120
-87 44 121 64 119
-88 45 122 65 120
-89 66 121 46 123
-90 34 122 47 124
-91 35 123 48 125
-92 36 124 49 126
-93 37 125 50 127
-94 38 126 51 128
-95 39 127 52 129
-96 40 128 53 130
-97 41 129 54 131
-98 55 132 42 130
-99 56 100 43 131
-100 99 143 68 156
-101 67 144 69 157
-102 68 145 70 158
-103 69 146 71 159
-104 70 147 72 160
-105 71 148 73 161
-106 72 149 74 162
-107 73 150 75 163
-108 74 151 76 164
-109 77 165 75 152
-110 78 133 76 153
-111 77 154 79 134
-112 78 155 80 135
-113 79 156 81 136
-114 80 157 82 137
-115 81 158 83 138
-116 82 159 84 139
-117 83 160 85 140
-118 84 161 86 141
-119 85 162 87 142
-120 88 143 86 163
-121 89 144 87 164
-122 88 165 90 145
-123 89 133 91 146
-124 90 134 92 147
-125 91 135 93 148
-126 92 136 94 149
-127 93 137 95 150
-128 94 138 96 151
-129 95 139 97 152
-130 96 140 98 153
-131 99 154 97 141
-132 67 155 98 142
-133 110 198 123 167
-134 111 166 124 168
-135 112 167 125 169
-136 113 168 126 170
-137 114 169 127 171
-138 115 170 128 172
-139 116 171 129 173
-140 117 172 130 174
-141 118 173 131 175
-142 132 176 119 174
-143 100 177 120 175
-144 121 176 101 178
-145 122 177 102 179
-146 123 178 103 180
-147 124 179 104 181
-148 125 180 105 182
-149 126 181 106 183
-150 127 182 107 184
-151 128 183 108 185
-152 129 184 109 186
-153 110 187 130 185
-154 111 188 131 186
-155 132 187 112 189
-156 100 188 113 190
-157 101 189 114 191
-158 102 190 115 192
-159 103 191 116 193
-160 104 192 117 194
-161 105 193 118 195
-162 106 194 119 196
-163 107 195 120 197
-164 121 198 108 196
-165 122 166 109 197
-166 11 165 24 134
-167 12 133 25 135
-168 13 134 26 136
-169 14 135 27 137
-170 15 136 28 138
-171 16 137 29 139
-172 17 138 30 140
-173 18 139 31 141
-174 19 140 32 142
-175 33 143 20 141
-176 1 144 21 142
-177 22 143 2 145
-178 23 144 3 146
-179 24 145 4 147
-180 25 146 5 148
-181 26 147 6 149
-182 27 148 7 150
-183 28 149 8 151
-184 29 150 9 152
-185 30 151 10 153
-186 11 154 31 152
-187 12 155 32 153
-188 33 154 13 156
-189 1 155 14 157
-190 2 156 15 158
-191 3 157 16 159
-192 4 158 17 160
-193 5 159 18 161
-194 6 160 19 162
-195 7 161 20 163
-196 8 162 21 164
-197 22 165 9 163
-198 23 133 10 164
0