Graph forms
for C4 [ 222, 5 ] = PS(6,37;10)
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On this page are computer-accessible forms for the graph C4[ 222, 5 ] =
PS(6,37;10).
(I) Following is a form readable by MAGMA:
g:=Graph<222|{ {148, 149}, {37, 38}, {65, 75}, {181, 191}, {180, 190}, {177,
187}, {176, 186}, {69, 79}, {68, 78}, {66, 76}, {179, 189}, {178, 188}, {67,
77}, {101, 112}, {103, 114}, {109, 120}, {111, 122}, {70, 80}, {71, 81}, {102,
113}, {110, 121}, {72, 82}, {73, 83}, {96, 122}, {97, 123}, {100, 126}, {101,
127}, {64, 91}, {164, 191}, {68, 95}, {104, 115}, {108, 119}, {160, 187}, {65,
92}, {163, 190}, {161, 188}, {67, 94}, {105, 116}, {107, 118}, {74, 84}, {98,
124}, {99, 125}, {66, 93}, {162, 189}, {106, 117}, {2, 38}, {3, 39}, {8, 44},
{9, 45}, {10, 46}, {11, 47}, {16, 52}, {17, 53}, {18, 54}, {19, 55}, {24, 60},
{25, 61}, {26, 62}, {27, 63}, {128, 164}, {129, 165}, {130, 166}, {131, 167},
{136, 172}, {137, 173}, {138, 174}, {139, 175}, {144, 180}, {145, 181}, {146,
182}, {147, 183}, {69, 96}, {71, 98}, {159, 186}, {1, 39}, {87, 113}, {86, 112},
{8, 46}, {9, 47}, {16, 54}, {17, 55}, {24, 62}, {25, 63}, {94, 120}, {95, 121},
{128, 166}, {129, 167}, {136, 174}, {137, 175}, {144, 182}, {145, 183}, {70,
97}, {2, 40}, {89, 115}, {88, 114}, {3, 41}, {6, 44}, {7, 45}, {18, 56}, {19,
57}, {22, 60}, {23, 61}, {92, 118}, {93, 119}, {130, 168}, {131, 169}, {134,
172}, {135, 173}, {146, 184}, {147, 185}, {72, 99}, {4, 40}, {5, 41}, {6, 42},
{7, 43}, {20, 56}, {21, 57}, {22, 58}, {23, 59}, {132, 168}, {133, 169}, {134,
170}, {135, 171}, {148, 184}, {73, 100}, {4, 42}, {5, 43}, {20, 58}, {21, 59},
{90, 116}, {91, 117}, {132, 170}, {133, 171}, {64, 111}, {74, 101}, {75, 123},
{79, 127}, {78, 126}, {77, 125}, {76, 124}, {10, 48}, {11, 49}, {14, 52}, {15,
53}, {138, 176}, {139, 177}, {142, 180}, {143, 181}, {12, 48}, {13, 49}, {14,
50}, {15, 51}, {140, 176}, {141, 177}, {142, 178}, {143, 179}, {12, 50}, {13,
51}, {140, 178}, {141, 179}, {38, 102}, {47, 111}, {46, 110}, {45, 109}, {44,
108}, {43, 107}, {42, 106}, {41, 105}, {40, 104}, {39, 103}, {149, 213}, {150,
214}, {151, 215}, {152, 216}, {153, 217}, {154, 218}, {155, 219}, {156, 220},
{157, 221}, {158, 222}, {1, 74}, {49, 96}, {63, 110}, {61, 108}, {59, 106}, {57,
104}, {55, 102}, {53, 100}, {51, 98}, {149, 196}, {151, 198}, {153, 200}, {155,
202}, {157, 204}, {159, 206}, {50, 97}, {62, 109}, {58, 105}, {54, 101}, {150,
197}, {154, 201}, {158, 205}, {52, 99}, {60, 107}, {156, 203}, {26, 64}, {27,
65}, {30, 68}, {31, 69}, {28, 64}, {29, 65}, {30, 66}, {31, 67}, {28, 66}, {29,
67}, {56, 103}, {152, 199}, {32, 68}, {35, 71}, {34, 70}, {33, 69}, {53, 80},
{183, 210}, {181, 208}, {175, 202}, {173, 200}, {167, 194}, {165, 192}, {63,
90}, {61, 88}, {55, 82}, {32, 70}, {33, 71}, {54, 81}, {182, 209}, {174, 201},
{166, 193}, {62, 89}, {34, 72}, {35, 73}, {56, 83}, {184, 211}, {172, 199},
{168, 195}, {60, 87}, {36, 72}, {37, 73}, {57, 84}, {185, 212}, {171, 198},
{169, 196}, {59, 86}, {36, 74}, {48, 95}, {170, 197}, {58, 85}, {160, 207}, {39,
86}, {175, 222}, {173, 220}, {171, 218}, {169, 216}, {167, 214}, {165, 212},
{163, 210}, {161, 208}, {47, 94}, {45, 92}, {43, 90}, {41, 88}, {38, 85}, {174,
221}, {170, 217}, {166, 213}, {162, 209}, {46, 93}, {42, 89}, {182, 192}, {183,
193}, {44, 91}, {172, 219}, {164, 211}, {184, 194}, {185, 195}, {48, 75}, {180,
207}, {176, 203}, {52, 79}, {49, 76}, {179, 206}, {177, 204}, {51, 78}, {40,
87}, {178, 205}, {168, 215}, {50, 77}, {32, 191}, {27, 186}, {29, 188}, {31,
190}, {30, 189}, {28, 187}, {16, 190}, {17, 191}, {14, 188}, {15, 189}, {12,
186}, {13, 187}, {75, 138}, {85, 148}, {83, 146}, {81, 144}, {79, 142}, {77,
140}, {78, 141}, {82, 145}, {1, 197}, {2, 198}, {3, 199}, {8, 204}, {9, 205},
{10, 206}, {11, 207}, {16, 212}, {17, 213}, {18, 214}, {19, 215}, {24, 220},
{25, 221}, {26, 222}, {76, 139}, {84, 147}, {112, 185}, {4, 200}, {5, 201}, {6,
202}, {7, 203}, {20, 216}, {21, 217}, {22, 218}, {23, 219}, {80, 128}, {88,
136}, {87, 135}, {86, 134}, {85, 133}, {84, 132}, {83, 131}, {82, 130}, {81,
129}, {89, 137}, {90, 138}, {91, 139}, {92, 140}, {93, 141}, {94, 142}, {95,
143}, {18, 192}, {19, 193}, {22, 196}, {23, 197}, {26, 200}, {27, 201}, {30,
204}, {31, 205}, {4, 215}, {8, 219}, {1, 212}, {3, 214}, {9, 220}, {11, 222},
{20, 194}, {21, 195}, {28, 202}, {29, 203}, {2, 213}, {10, 221}, {122, 160},
{123, 161}, {126, 164}, {127, 165}, {12, 208}, {13, 209}, {14, 210}, {15, 211},
{124, 160}, {125, 161}, {126, 162}, {127, 163}, {5, 216}, {7, 218}, {24, 198},
{25, 199}, {124, 162}, {125, 163}, {6, 217}, {80, 143}, {33, 192}, {37, 196},
{35, 194}, {34, 193}, {113, 149}, {114, 150}, {115, 151}, {120, 156}, {121,
157}, {122, 158}, {123, 159}, {102, 128}, {103, 129}, {110, 136}, {111, 137},
{112, 150}, {113, 151}, {120, 158}, {121, 159}, {36, 195}, {104, 130}, {105,
131}, {108, 134}, {109, 135}, {114, 152}, {115, 153}, {118, 156}, {119, 157},
{116, 152}, {117, 153}, {118, 154}, {119, 155}, {32, 206}, {33, 207}, {106,
132}, {107, 133}, {116, 154}, {117, 155}, {96, 144}, {97, 145}, {98, 146}, {99,
147}, {100, 148}, {34, 208}, {35, 209}, {36, 210}, {37, 211} }>;
(II) A more general form is to represent the graph as the orbit of {148, 149}
under the group generated by the following permutations:
a: (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37)(38, 39, 40, 41,
42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61,
62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74)(75, 76, 77, 78, 79, 80, 81,
82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100,
101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111)(112, 113, 114, 115, 116,
117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132,
133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147,
148)(149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163,
164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179,
180, 181, 182, 183, 184, 185)(186, 187, 188, 189, 190, 191, 192, 193, 194, 195,
196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211,
212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222) (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, 37)(3, 36)(4, 35)(5, 34)(6, 33)(7, 32)(8, 31)(9, 30)(10, 29)(11, 28)(12,
27)(13, 26)(14, 25)(15, 24)(16, 23)(17, 22)(18, 21)(19, 20)(39, 74)(40, 73)(41,
72)(42, 71)(43, 70)(44, 69)(45, 68)(46, 67)(47, 66)(48, 65)(49, 64)(50, 63)(51,
62)(52, 61)(53, 60)(54, 59)(55, 58)(56, 57)(76, 111)(77, 110)(78, 109)(79,
108)(80, 107)(81, 106)(82, 105)(83, 104)(84, 103)(85, 102)(86, 101)(87, 100)(88,
99)(89, 98)(90, 97)(91, 96)(92, 95)(93, 94)(113, 148)(114, 147)(115, 146)(116,
145)(117, 144)(118, 143)(119, 142)(120, 141)(121, 140)(122, 139)(123, 138)(124,
137)(125, 136)(126, 135)(127, 134)(128, 133)(129, 132)(130, 131)(150, 185)(151,
184)(152, 183)(153, 182)(154, 181)(155, 180)(156, 179)(157, 178)(158, 177)(159,
176)(160, 175)(161, 174)(162, 173)(163, 172)(164, 171)(165, 170)(166, 169)(167,
168)(187, 222)(188, 221)(189, 220)(190, 219)(191, 218)(192, 217)(193, 216)(194,
215)(195, 214)(196, 213)(197, 212)(198, 211)(199, 210)(200, 209)(201, 208)(202,
207)(203, 206)(204, 205)
c: (1, 38, 75, 112, 149, 186)(2, 65, 101, 148, 159, 197)(3, 55, 90, 147, 169,
208)(4, 45, 79, 146, 179, 219)(5, 72, 105, 145, 152, 193)(6, 62, 94, 144, 162,
204)(7, 52, 83, 143, 172, 215)(8, 42, 109, 142, 182, 189)(9, 69, 98, 141, 155,
200)(10, 59, 87, 140, 165, 211)(11, 49, 76, 139, 175, 222)(12, 39, 102, 138,
185, 196)(13, 66, 91, 137, 158, 207)(14, 56, 80, 136, 168, 218)(15, 46, 106,
135, 178, 192)(16, 73, 95, 134, 151, 203)(17, 63, 84, 133, 161, 214)(18, 53,
110, 132, 171, 188)(19, 43, 99, 131, 181, 199)(20, 70, 88, 130, 154, 210)(21,
60, 77, 129, 164, 221)(22, 50, 103, 128, 174, 195)(23, 40, 92, 127, 184,
206)(24, 67, 81, 126, 157, 217)(25, 57, 107, 125, 167, 191)(26, 47, 96, 124,
177, 202)(27, 74, 85, 123, 150, 213)(28, 64, 111, 122, 160, 187)(29, 54, 100,
121, 170, 198)(30, 44, 89, 120, 180, 209)(31, 71, 78, 119, 153, 220)(32, 61,
104, 118, 163, 194)(33, 51, 93, 117, 173, 205)(34, 41, 82, 116, 183, 216)(35,
68, 108, 115, 156, 190)(36, 58, 97, 114, 166, 201)(37, 48, 86, 113, 176,
212)
C4[ 222, 5 ]
222
-1 212 39 74 197
-2 198 213 38 40
-3 199 214 39 41
-4 200 215 40 42
-5 201 216 41 43
-6 44 202 217 42
-7 45 203 218 43
-8 44 46 204 219
-9 220 45 47 205
-10 221 46 48 206
-11 222 47 49 207
-12 48 50 186 208
-13 187 209 49 51
-14 188 210 50 52
-15 189 211 51 53
-16 190 212 52 54
-17 55 191 213 53
-18 56 192 214 54
-19 55 57 193 215
-20 56 58 194 216
-21 57 59 195 217
-22 58 60 196 218
-23 59 61 197 219
-24 198 220 60 62
-25 199 221 61 63
-26 200 222 62 64
-27 201 63 65 186
-28 66 187 202 64
-29 67 188 203 65
-30 66 68 189 204
-31 67 69 190 205
-32 68 70 191 206
-33 69 71 192 207
-34 70 72 193 208
-35 209 71 73 194
-36 210 72 74 195
-37 211 38 73 196
-38 2 102 37 85
-39 1 3 103 86
-40 2 4 104 87
-41 88 3 5 105
-42 89 4 6 106
-43 90 5 7 107
-44 91 6 8 108
-45 92 7 9 109
-46 110 93 8 10
-47 11 111 94 9
-48 12 95 75 10
-49 11 13 96 76
-50 77 12 14 97
-51 78 13 15 98
-52 99 79 14 16
-53 100 80 15 17
-54 101 81 16 18
-55 102 82 17 19
-56 103 83 18 20
-57 104 84 19 21
-58 22 105 85 20
-59 23 106 86 21
-60 22 24 107 87
-61 88 23 25 108
-62 89 24 26 109
-63 110 90 25 27
-64 111 91 26 28
-65 92 27 29 75
-66 93 28 30 76
-67 77 94 29 31
-68 78 95 30 32
-69 33 79 96 31
-70 34 80 97 32
-71 33 35 81 98
-72 99 34 36 82
-73 100 35 37 83
-74 1 101 36 84
-75 123 48 138 65
-76 66 124 49 139
-77 67 125 50 140
-78 68 126 51 141
-79 69 127 52 142
-80 143 70 128 53
-81 144 71 129 54
-82 55 145 72 130
-83 56 146 73 131
-84 132 57 147 74
-85 133 58 38 148
-86 112 134 59 39
-87 113 135 60 40
-88 114 136 61 41
-89 115 137 62 42
-90 116 138 63 43
-91 44 117 139 64
-92 45 118 140 65
-93 66 46 119 141
-94 67 47 120 142
-95 121 143 68 48
-96 122 144 69 49
-97 123 145 70 50
-98 124 146 71 51
-99 125 147 72 52
-100 126 148 73 53
-101 112 127 74 54
-102 55 113 38 128
-103 56 114 39 129
-104 57 115 40 130
-105 58 116 41 131
-106 132 59 117 42
-107 133 60 118 43
-108 44 134 61 119
-109 45 135 62 120
-110 121 46 136 63
-111 122 47 137 64
-112 101 150 86 185
-113 102 149 151 87
-114 88 103 150 152
-115 89 104 151 153
-116 154 90 105 152
-117 155 91 106 153
-118 154 156 92 107
-119 155 157 93 108
-120 156 158 94 109
-121 110 157 159 95
-122 111 158 160 96
-123 159 161 75 97
-124 160 162 76 98
-125 77 99 161 163
-126 78 100 162 164
-127 165 79 101 163
-128 166 80 102 164
-129 165 167 81 103
-130 166 168 82 104
-131 167 169 83 105
-132 168 170 84 106
-133 169 171 85 107
-134 170 172 86 108
-135 171 173 87 109
-136 88 110 172 174
-137 89 111 173 175
-138 176 90 75 174
-139 177 91 76 175
-140 77 176 178 92
-141 78 177 179 93
-142 79 178 180 94
-143 80 179 181 95
-144 81 180 182 96
-145 82 181 183 97
-146 83 182 184 98
-147 99 84 183 185
-148 100 149 85 184
-149 113 213 148 196
-150 112 114 214 197
-151 198 113 115 215
-152 199 114 116 216
-153 200 115 117 217
-154 201 116 118 218
-155 202 117 119 219
-156 220 203 118 120
-157 121 221 204 119
-158 122 222 205 120
-159 121 123 206 186
-160 187 122 124 207
-161 188 123 125 208
-162 209 189 124 126
-163 210 190 125 127
-164 211 191 126 128
-165 212 192 127 129
-166 213 193 128 130
-167 214 194 129 131
-168 132 215 195 130
-169 133 216 196 131
-170 132 134 217 197
-171 198 133 135 218
-172 199 134 136 219
-173 220 200 135 137
-174 221 201 136 138
-175 222 202 137 139
-176 203 138 140 186
-177 187 204 139 141
-178 188 205 140 142
-179 143 189 206 141
-180 144 190 207 142
-181 143 145 191 208
-182 209 144 146 192
-183 210 145 147 193
-184 211 146 148 194
-185 112 212 147 195
-186 176 12 27 159
-187 177 13 28 160
-188 178 14 29 161
-189 179 15 30 162
-190 180 16 31 163
-191 181 17 32 164
-192 33 165 182 18
-193 34 166 183 19
-194 35 167 184 20
-195 36 168 185 21
-196 22 37 169 149
-197 1 23 170 150
-198 2 24 171 151
-199 3 25 172 152
-200 4 26 173 153
-201 154 5 27 174
-202 155 6 28 175
-203 176 156 7 29
-204 177 157 8 30
-205 178 158 9 31
-206 179 159 10 32
-207 11 33 180 160
-208 12 34 181 161
-209 13 35 182 162
-210 14 36 183 163
-211 15 37 184 164
-212 165 1 16 185
-213 166 2 17 149
-214 167 3 18 150
-215 168 4 19 151
-216 169 5 20 152
-217 170 6 21 153
-218 22 154 171 7
-219 23 155 172 8
-220 24 156 173 9
-221 25 157 174 10
-222 11 26 158 175
0