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