Graph forms
for C4 [ 224, 20 ] =
PL(MC3(14,8,1,5,3,4,1),[4^28,28^4])
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On this page are computer-accessible forms for the graph C4[ 224, 20 ] =
PL(MC3(14,8,1,5,3,4,1),[4^28,28^4]).
(I) Following is a form readable by MAGMA:
g:=Graph<224|{ {112, 115}, {112, 122}, {105, 121}, {108, 124}, {102, 116}, {109,
127}, {98, 118}, {108, 120}, {106, 126}, {103, 115}, {102, 114}, {99, 119},
{110, 123}, {107, 125}, {111, 121}, {100, 124}, {104, 114}, {111, 117}, {98,
126}, {107, 119}, {106, 118}, {105, 117}, {104, 116}, {100, 120}, {103, 122},
{99, 125}, {110, 113}, {92, 127}, {94, 123}, {94, 113}, {18, 114}, {30, 126},
{26, 120}, {18, 113}, {26, 126}, {30, 120}, {16, 119}, {19, 116}, {19, 123}, {3,
115}, {7, 117}, {9, 123}, {6, 117}, {2, 118}, {8, 125}, {1, 118}, {10, 125}, {4,
115}, {14, 119}, {3, 121}, {5, 127}, {6, 122}, {1, 124}, {15, 114}, {9, 116},
{7, 122}, {4, 121}, {1, 127}, {15, 113}, {2, 124}, {14, 142}, {77, 205}, {48,
176}, {39, 167}, {21, 148}, {74, 203}, {31, 157}, {78, 204}, {76, 206}, {81,
210}, {24, 156}, {8, 141}, {49, 180}, {14, 137}, {10, 130}, {88, 208}, {29,
149}, {25, 145}, {34, 171}, {36, 173}, {8, 130}, {79, 197}, {35, 169}, {74,
193}, {38, 170}, {44, 161}, {78, 195}, {45, 160}, {33, 175}, {43, 165}, {42,
164}, {26, 149}, {77, 194}, {41, 166}, {32, 176}, {91, 203}, {37, 181}, {36,
180}, {55, 167}, {67, 211}, {73, 217}, {9, 152}, {64, 209}, {68, 213}, {32,
178}, {94, 204}, {67, 209}, {69, 215}, {72, 218}, {11, 152}, {93, 206}, {65,
210}, {28, 136}, {37, 177}, {65, 213}, {66, 214}, {3, 150}, {83, 198}, {82,
199}, {27, 142}, {12, 153}, {28, 138}, {19, 132}, {90, 205}, {47, 184}, {27,
140}, {23, 128}, {20, 131}, {72, 223}, {28, 132}, {90, 194}, {87, 207}, {81,
201}, {33, 185}, {16, 137}, {89, 192}, {22, 143}, {20, 141}, {19, 138}, {57,
160}, {69, 220}, {5, 159}, {95, 197}, {91, 193}, {80, 202}, {53, 175}, {36,
190}, {6, 156}, {61, 167}, {62, 164}, {13, 150}, {79, 212}, {38, 189}, {29,
134}, {59, 160}, {26, 134}, {88, 196}, {51, 175}, {49, 173}, {54, 170}, {64,
220}, {65, 221}, {28, 129}, {94, 195}, {85, 200}, {60, 161}, {1, 159}, {34,
188}, {52, 171}, {66, 221}, {68, 219}, {17, 177}, {45, 140}, {54, 151}, {17,
179}, {100, 198}, {53, 151}, {17, 181}, {99, 199}, {43, 143}, {39, 131}, {31,
187}, {11, 174}, {46, 139}, {24, 189}, {13, 168}, {12, 169}, {63, 154}, {17,
183}, {46, 136}, {9, 174}, {31, 184}, {55, 144}, {71, 224}, {23, 191}, {103,
207}, {97, 201}, {105, 192}, {6, 172}, {98, 200}, {96, 202}, {56, 146}, {57,
147}, {3, 168}, {48, 155}, {46, 133}, {8, 163}, {59, 144}, {14, 162}, {104,
196}, {44, 128}, {30, 178}, {51, 158}, {16, 190}, {52, 154}, {60, 146}, {61,
147}, {40, 135}, {46, 129}, {10, 187}, {38, 151}, {21, 164}, {58, 139}, {47,
157}, {55, 133}, {57, 139}, {22, 165}, {2, 182}, {24, 172}, {13, 185}, {12,
186}, {23, 161}, {11, 188}, {39, 144}, {20, 163}, {2, 186}, {104, 208}, {41,
145}, {34, 154}, {15, 183}, {27, 162}, {5, 191}, {40, 146}, {35, 153}, {12,
182}, {58, 128}, {32, 155}, {15, 179}, {58, 135}, {42, 148}, {45, 147}, {25,
166}, {33, 158}, {56, 135}, {58, 133}, {62, 129}, {4, 196}, {72, 136}, {11,
202}, {10, 200}, {110, 172}, {71, 133}, {73, 139}, {112, 179}, {7, 195}, {90,
159}, {73, 143}, {87, 145}, {75, 140}, {95, 152}, {4, 204}, {106, 162}, {13,
197}, {75, 131}, {25, 208}, {42, 224}, {86, 156}, {83, 153}, {75, 128}, {75,
135}, {96, 172}, {88, 148}, {5, 203}, {102, 168}, {85, 155}, {80, 158}, {78,
129}, {108, 163}, {97, 174}, {90, 149}, {82, 157}, {88, 136}, {93, 141}, {92,
140}, {24, 201}, {96, 177}, {70, 151}, {18, 192}, {97, 179}, {22, 196}, {29,
206}, {101, 182}, {89, 138}, {87, 132}, {21, 192}, {91, 142}, {79, 154}, {16,
198}, {89, 143}, {71, 145}, {7, 208}, {101, 178}, {31, 200}, {55, 224}, {69,
157}, {111, 183}, {97, 185}, {20, 205}, {99, 186}, {30, 199}, {27, 194}, {74,
147}, {21, 207}, {92, 134}, {25, 195}, {22, 204}, {66, 153}, {23, 203}, {98,
190}, {29, 193}, {60, 224}, {72, 148}, {76, 144}, {18, 207}, {64, 158}, {112,
174}, {68, 155}, {100, 187}, {92, 131}, {77, 146}, {50, 210}, {84, 180}, {54,
214}, {57, 217}, {62, 222}, {48, 209}, {80, 177}, {50, 211}, {36, 198}, {108,
142}, {95, 189}, {93, 191}, {84, 182}, {53, 215}, {56, 218}, {71, 165}, {50,
209}, {105, 138}, {103, 132}, {86, 181}, {83, 176}, {52, 215}, {59, 216}, {61,
222}, {33, 197}, {109, 137}, {49, 213}, {59, 223}, {63, 219}, {60, 217}, {40,
206}, {84, 178}, {53, 211}, {51, 213}, {50, 212}, {62, 216}, {32, 199}, {106,
141}, {101, 130}, {56, 223}, {61, 218}, {34, 202}, {95, 183}, {83, 187}, {82,
186}, {81, 185}, {52, 220}, {51, 219}, {69, 173}, {40, 193}, {63, 214}, {70,
175}, {39, 205}, {86, 188}, {78, 164}, {64, 170}, {65, 171}, {54, 221}, {109,
134}, {85, 190}, {63, 212}, {48, 220}, {101, 137}, {84, 184}, {77, 161}, {49,
221}, {76, 160}, {68, 169}, {74, 167}, {38, 201}, {109, 130}, {45, 194}, {73,
166}, {35, 211}, {37, 212}, {43, 218}, {41, 216}, {44, 222}, {87, 165}, {79,
189}, {66, 176}, {42, 217}, {70, 181}, {76, 191}, {35, 215}, {107, 159}, {47,
219}, {44, 216}, {43, 222}, {41, 223}, {96, 150}, {37, 210}, {111, 152}, {67,
180}, {91, 163}, {110, 150}, {47, 214}, {70, 188}, {102, 156}, {81, 171}, {80,
170}, {67, 184}, {85, 169}, {86, 168}, {107, 149}, {82, 173}, {93, 162}, {89,
166} }>;
(II) A more general form is to represent the graph as the orbit of {112, 115}
under the group generated by the following permutations:
a: (8, 14)(10, 16)(20, 27)(31, 36)(39, 45)(47, 49)(55, 57)(63, 65)(71, 73)(79,
81)(87, 89)(95, 97)(103, 105)(111, 112)(115, 121)(117, 122)(119, 125)(130,
137)(131, 140)(132, 138)(133, 139)(141, 162)(142, 163)(143, 165)(144, 160)(145,
166)(147, 167)(152, 174)(154, 171)(157, 173)(179, 183)(180, 184)(185, 197)(187,
198)(189, 201)(190, 200)(192, 207)(194, 205)(210, 212)(213, 219)(214, 221)(217,
224) (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, 5)(3, 9, 6, 15)(4, 11, 7, 17)(10, 20)(12, 23)(13, 19, 24, 18)(16, 27)(21,
33, 28, 38)(22, 34, 25, 37)(29, 30)(31, 39)(32, 40)(35, 44)(36, 45)(41, 50, 43,
52)(42, 51, 46, 54)(47, 55)(48, 56)(49, 57)(53, 62)(58, 66, 60, 68)(59, 67, 61,
69)(63, 71)(64, 72)(65, 73)(70, 78)(74, 82, 76, 84)(75, 83, 77, 85)(79, 87)(80,
88)(81, 89)(86, 94)(90, 98, 92, 100)(91, 99, 93, 101)(95, 103)(96, 104)(97,
105)(102, 110)(106, 109, 108, 107)(111, 112)(113, 168, 123, 156)(114, 150, 116,
172)(115, 152, 122, 183)(117, 179, 121, 174)(118, 127, 124, 159)(119, 162, 137,
142)(120, 149, 126, 134)(125, 141, 130, 163)(128, 153, 161, 169)(129, 151, 164,
175)(131, 187, 205, 200)(132, 189, 207, 197)(133, 214, 224, 219)(135, 176, 146,
155)(136, 170, 148, 158)(138, 201, 192, 185)(139, 221, 217, 213)(140, 198, 194,
190)(143, 171, 166, 210)(144, 184, 167, 157)(145, 212, 165, 154)(147, 173, 160,
180)(177, 196, 202, 208)(178, 193, 199, 206)(181, 204, 188, 195)(182, 203, 186,
191)(209, 218, 220, 223)(211, 222, 215, 216)
c: (3, 6)(4, 7)(8, 14)(10, 16)(13, 24)(20, 27)(22, 25)(31, 36)(33, 38)(39,
45)(41, 43)(47, 49)(51, 54)(55, 57)(59, 61)(63, 65)(66, 68)(71, 73)(74, 76)(79,
81)(83, 85)(87, 89)(91, 93)(95, 97)(98, 100)(103, 105)(106, 108)(111, 112)(115,
117)(118, 124)(119, 125)(120, 126)(121, 122)(130, 137)(131, 140)(132, 138)(133,
139)(141, 142)(143, 145)(144, 147)(150, 172)(151, 175)(152, 174)(153, 169)(154,
171)(155, 176)(156, 168)(157, 173)(158, 170)(160, 167)(162, 163)(165, 166)(179,
183)(180, 184)(185, 189)(187, 190)(191, 203)(192, 207)(193, 206)(194, 205)(195,
204)(196, 208)(197, 201)(198, 200)(210, 212)(213, 214)(216, 222)(217, 224)(218,
223)(219, 221)
d: (1, 2)(3, 4)(5, 12)(6, 7)(8, 16)(9, 19)(10, 14)(11, 28)(13, 22)(15, 18)(17,
21)(20, 36)(23, 35)(24, 25)(26, 30)(27, 31)(29, 32)(33, 43)(34, 46)(37, 42)(38,
41)(39, 49)(40, 48)(44, 53)(45, 47)(50, 60)(51, 61)(52, 58)(54, 59)(55, 65)(56,
64)(57, 63)(62, 70)(66, 76)(67, 77)(68, 74)(69, 75)(71, 81)(72, 80)(73, 79)(78,
86)(82, 92)(83, 93)(84, 90)(85, 91)(87, 97)(88, 96)(89, 95)(94, 102)(98,
108)(99, 109)(100, 106)(101, 107)(103, 112)(104, 110)(105, 111)(113, 114)(116,
123)(118, 124)(119, 130)(120, 126)(125, 137)(127, 186)(128, 215)(129, 188)(131,
173)(132, 174)(133, 171)(134, 199)(135, 220)(136, 202)(138, 152)(139, 154)(140,
157)(141, 198)(142, 200)(143, 197)(144, 221)(145, 201)(146, 209)(147, 219)(148,
177)(149, 178)(150, 196)(151, 216)(153, 191)(155, 193)(156, 195)(158, 218)(159,
182)(160, 214)(161, 211)(162, 187)(163, 190)(164, 181)(165, 185)(166, 189)(167,
213)(168, 204)(169, 203)(170, 223)(172, 208)(175, 222)(176, 206)(179, 207)(180,
205)(183, 192)(184, 194)(210, 224)(212, 217)
e: (9, 15)(11, 17)(18, 19)(21, 28)(34, 37)(42, 46)(50, 52)(58, 60)(67, 69)(75,
77)(82, 84)(90, 92)(99, 101)(107, 109)(113, 123)(114, 116)(119, 137)(125,
130)(127, 159)(128, 161)(129, 164)(131, 205)(132, 207)(133, 224)(134, 149)(135,
146)(136, 148)(138, 192)(139, 217)(140, 194)(152, 183)(154, 212)(157, 184)(171,
210)(173, 180)(174, 179)(177, 202)(178, 199)(181, 188)(182, 186)(209, 220)(211,
215)
f: (1, 3, 14, 15, 26, 6, 8, 9)(2, 4, 16, 18, 30, 7, 10, 19)(5, 13, 27, 17, 29,
24, 20, 11)(12, 22, 36, 21, 32, 25, 31, 28)(23, 33, 45, 37, 40, 38, 39, 34)(35,
43, 49, 42, 48, 41, 47, 46)(44, 51, 57, 50, 56, 54, 55, 52)(53, 61, 65, 60, 64,
59, 63, 58)(62, 68, 73, 67, 72, 66, 71, 69)(70, 74, 81, 77, 80, 76, 79, 75)(78,
85, 89, 84, 88, 83, 87, 82)(86, 91, 97, 90, 96, 93, 95, 92)(94, 98, 105, 101,
104, 100, 103, 99)(102, 108, 112, 107, 110, 106, 111, 109)(113, 126, 117, 130,
116, 124, 115, 119)(114, 120, 122, 125, 123, 118, 121, 137)(127, 168, 142, 179,
149, 172, 141, 152)(128, 175, 147, 210, 146, 170, 144, 154)(129, 169, 143, 180,
148, 176, 145, 157)(131, 188, 203, 185, 194, 177, 206, 189)(132, 186, 204, 190,
192, 178, 208, 187)(133, 215, 222, 213, 217, 209, 223, 214)(134, 156, 163, 174,
159, 150, 162, 183)(135, 151, 167, 171, 161, 158, 160, 212)(136, 153, 165, 173,
164, 155, 166, 184)(138, 182, 196, 198, 207, 199, 195, 200)(139, 211, 218, 221,
224, 220, 216, 219)(140, 181, 193, 201, 205, 202, 191, 197)
C4[ 224, 20 ]
224
-1 124 159 127 118
-2 124 182 118 186
-3 121 168 115 150
-4 121 115 204 196
-5 191 159 203 127
-6 122 156 117 172
-7 122 117 195 208
-8 125 130 141 163
-9 123 116 152 174
-10 187 200 125 130
-11 188 202 152 174
-12 169 182 153 186
-13 168 150 185 197
-14 137 162 119 142
-15 113 179 114 183
-16 198 190 137 119
-17 177 179 181 183
-18 113 114 192 207
-19 132 123 116 138
-20 205 141 163 131
-21 148 192 207 164
-22 143 165 204 196
-23 191 203 128 161
-24 156 189 201 172
-25 166 145 195 208
-26 134 126 149 120
-27 194 140 162 142
-28 132 136 138 129
-29 134 149 193 206
-30 199 178 126 120
-31 187 200 157 184
-32 176 155 199 178
-33 158 185 175 197
-34 154 188 202 171
-35 211 169 215 153
-36 198 190 180 173
-37 177 210 212 181
-38 189 201 170 151
-39 144 167 205 131
-40 135 146 193 206
-41 166 145 223 216
-42 224 148 217 164
-43 143 165 222 218
-44 222 128 161 216
-45 147 160 194 140
-46 133 136 139 129
-47 157 214 184 219
-48 176 209 220 155
-49 221 180 213 173
-50 209 210 211 212
-51 158 213 175 219
-52 154 220 171 215
-53 211 215 151 175
-54 221 170 214 151
-55 133 144 167 224
-56 135 146 223 218
-57 147 160 139 217
-58 133 135 128 139
-59 144 223 160 216
-60 146 224 161 217
-61 167 222 147 218
-62 222 216 129 164
-63 154 212 214 219
-64 209 220 158 170
-65 210 221 213 171
-66 176 221 214 153
-67 209 211 180 184
-68 155 169 213 219
-69 220 157 215 173
-70 188 181 151 175
-71 165 133 145 224
-72 223 136 148 218
-73 143 166 139 217
-74 167 147 203 193
-75 135 128 140 131
-76 144 191 160 206
-77 146 161 194 205
-78 204 129 195 164
-79 154 189 212 197
-80 177 158 202 170
-81 210 201 171 185
-82 199 157 173 186
-83 176 187 198 153
-84 178 180 182 184
-85 155 200 190 169
-86 188 156 168 181
-87 132 165 145 207
-88 136 148 196 208
-89 143 166 192 138
-90 159 149 194 205
-91 203 193 163 142
-92 134 127 140 131
-93 191 162 206 141
-94 123 113 204 195
-95 189 183 152 197
-96 177 202 150 172
-97 179 201 174 185
-98 200 190 126 118
-99 199 125 119 186
-100 187 198 124 120
-101 178 137 182 130
-102 156 168 114 116
-103 132 122 115 207
-104 114 116 196 208
-105 121 192 138 117
-106 126 118 162 141
-107 125 159 149 119
-108 124 163 120 142
-109 134 137 127 130
-110 123 113 150 172
-111 121 117 183 152
-112 122 179 115 174
-113 110 15 94 18
-114 102 15 104 18
-115 112 3 4 103
-116 102 104 19 9
-117 111 6 105 7
-118 1 2 106 98
-119 99 14 16 107
-120 100 26 30 108
-121 111 3 4 105
-122 112 103 6 7
-123 110 94 19 9
-124 1 100 2 108
-125 99 8 107 10
-126 26 106 30 98
-127 1 92 5 109
-128 44 23 58 75
-129 78 46 28 62
-130 101 8 10 109
-131 92 39 20 75
-132 103 28 19 87
-133 55 46 58 71
-134 26 92 29 109
-135 56 58 40 75
-136 88 46 28 72
-137 101 14 16 109
-138 89 28 105 19
-139 46 57 58 73
-140 45 92 27 75
-141 93 106 8 20
-142 14 91 27 108
-143 22 89 73 43
-144 55 59 39 76
-145 25 71 41 87
-146 77 56 60 40
-147 45 57 61 74
-148 88 72 42 21
-149 90 26 29 107
-150 110 13 3 96
-151 70 38 53 54
-152 11 111 95 9
-153 66 12 35 83
-154 34 79 52 63
-155 68 48 85 32
-156 24 102 6 86
-157 47 69 82 31
-158 33 80 51 64
-159 1 90 5 107
-160 45 57 59 76
-161 44 77 23 60
-162 14 27 93 106
-163 91 8 20 108
-164 78 62 42 21
-165 22 71 43 87
-166 89 25 73 41
-167 55 39 61 74
-168 13 3 102 86
-169 12 35 68 85
-170 80 38 64 54
-171 34 81 52 65
-172 110 24 6 96
-173 36 69 49 82
-174 11 112 9 97
-175 33 70 51 53
-176 66 48 83 32
-177 80 37 17 96
-178 101 84 30 32
-179 112 15 17 97
-180 67 36 49 84
-181 37 70 17 86
-182 12 2 101 84
-183 111 15 17 95
-184 67 47 84 31
-185 33 13 81 97
-186 99 12 2 82
-187 100 83 31 10
-188 11 34 70 86
-189 24 79 38 95
-190 36 16 85 98
-191 23 5 93 76
-192 89 105 18 21
-193 91 29 40 74
-194 77 45 90 27
-195 78 25 94 7
-196 22 88 4 104
-197 33 13 79 95
-198 100 36 16 83
-199 99 82 30 32
-200 85 31 10 98
-201 24 81 38 97
-202 11 34 80 96
-203 23 91 5 74
-204 22 78 4 94
-205 77 90 39 20
-206 93 29 40 76
-207 103 18 21 87
-208 88 25 104 7
-209 67 48 50 64
-210 37 81 50 65
-211 67 35 50 53
-212 79 37 50 63
-213 68 49 51 65
-214 66 47 63 54
-215 35 69 52 53
-216 44 59 62 41
-217 57 60 73 42
-218 56 61 72 43
-219 68 47 51 63
-220 69 48 52 64
-221 66 49 54 65
-222 44 61 62 43
-223 56 59 72 41
-224 55 60 71 42
0