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