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