Graph forms
for C4 [ 240, 41 ] = MSZ(20,12,3,5)
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On this page are computer-accessible forms for the graph C4[ 240, 41 ] =
MSZ(20,12,3,5).
(I) Following is a form readable by MAGMA:
g:=Graph<240|{ {2, 3}, {238, 239}, {236, 237}, {234, 235}, {232, 233}, {230,
231}, {228, 229}, {226, 227}, {224, 225}, {222, 223}, {218, 219}, {216, 217},
{214, 215}, {212, 213}, {210, 211}, {208, 209}, {206, 207}, {204, 205}, {202,
203}, {198, 199}, {196, 197}, {194, 195}, {192, 193}, {190, 191}, {188, 189},
{186, 187}, {184, 185}, {182, 183}, {178, 179}, {176, 177}, {174, 175}, {172,
173}, {170, 171}, {168, 169}, {166, 167}, {164, 165}, {162, 163}, {158, 159},
{156, 157}, {154, 155}, {84, 85}, {82, 83}, {78, 79}, {76, 77}, {74, 75}, {72,
73}, {70, 71}, {68, 69}, {66, 67}, {64, 65}, {62, 63}, {58, 59}, {56, 57}, {54,
55}, {52, 53}, {50, 51}, {4, 5}, {6, 7}, {8, 9}, {10, 11}, {12, 13}, {14, 15},
{16, 17}, {18, 19}, {22, 23}, {24, 25}, {26, 27}, {28, 29}, {30, 31}, {32, 33},
{34, 35}, {36, 37}, {38, 39}, {42, 43}, {44, 45}, {46, 47}, {48, 49}, {86, 87},
{88, 89}, {90, 91}, {92, 93}, {94, 95}, {96, 97}, {98, 99}, {102, 103}, {104,
105}, {106, 107}, {108, 109}, {110, 111}, {112, 113}, {114, 115}, {116, 117},
{118, 119}, {122, 123}, {124, 125}, {126, 127}, {128, 129}, {130, 131}, {132,
133}, {134, 135}, {136, 137}, {138, 139}, {142, 143}, {144, 145}, {146, 147},
{148, 149}, {150, 151}, {152, 153}, {1, 2}, {237, 238}, {233, 234}, {229, 230},
{225, 226}, {221, 222}, {220, 223}, {217, 218}, {213, 214}, {209, 210}, {205,
206}, {201, 202}, {200, 203}, {197, 198}, {193, 194}, {189, 190}, {185, 186},
{181, 182}, {180, 183}, {177, 178}, {173, 174}, {169, 170}, {165, 166}, {161,
162}, {160, 163}, {157, 158}, {153, 154}, {81, 82}, {80, 83}, {77, 78}, {73,
74}, {69, 70}, {65, 66}, {61, 62}, {60, 63}, {57, 58}, {53, 54}, {5, 6}, {9,
10}, {13, 14}, {17, 18}, {20, 23}, {21, 22}, {25, 26}, {29, 30}, {33, 34}, {37,
38}, {40, 43}, {41, 42}, {45, 46}, {49, 50}, {85, 86}, {89, 90}, {93, 94}, {97,
98}, {100, 103}, {101, 102}, {105, 106}, {109, 110}, {113, 114}, {117, 118},
{120, 123}, {121, 122}, {125, 126}, {129, 130}, {133, 134}, {137, 138}, {140,
143}, {141, 142}, {145, 146}, {149, 150}, {3, 4}, {235, 236}, {227, 228}, {219,
220}, {218, 221}, {211, 212}, {203, 204}, {195, 196}, {187, 188}, {179, 180},
{178, 181}, {171, 172}, {163, 164}, {155, 156}, {83, 84}, {75, 76}, {67, 68},
{59, 60}, {58, 61}, {51, 52}, {11, 12}, {18, 21}, {19, 20}, {27, 28}, {35, 36},
{43, 44}, {91, 92}, {98, 101}, {99, 100}, {107, 108}, {115, 116}, {123, 124},
{131, 132}, {138, 141}, {139, 140}, {147, 148}, {7, 8}, {231, 232}, {215, 216},
{199, 200}, {198, 201}, {183, 184}, {167, 168}, {71, 72}, {55, 56}, {23, 24},
{38, 41}, {39, 40}, {87, 88}, {103, 104}, {118, 121}, {119, 120}, {135, 136},
{151, 152}, {1, 20}, {201, 220}, {161, 180}, {41, 60}, {8, 31}, {192, 215},
{168, 191}, {72, 95}, {64, 87}, {32, 55}, {96, 119}, {104, 127}, {128, 151},
{136, 159}, {2, 25}, {194, 217}, {166, 189}, {162, 185}, {70, 93}, {66, 89}, {6,
29}, {34, 57}, {102, 125}, {130, 153}, {134, 157}, {101, 120}, {4, 27}, {239,
240}, {207, 208}, {196, 219}, {175, 176}, {164, 187}, {79, 80}, {78, 81}, {68,
91}, {15, 16}, {36, 59}, {47, 48}, {111, 112}, {132, 155}, {143, 144}, {10, 33},
{206, 229}, {202, 225}, {154, 177}, {74, 97}, {14, 37}, {26, 49}, {30, 53}, {90,
113}, {94, 117}, {142, 165}, {141, 160}, {221, 240}, {12, 35}, {204, 227}, {156,
179}, {76, 99}, {28, 51}, {92, 115}, {81, 100}, {16, 39}, {216, 239}, {208,
231}, {152, 175}, {24, 47}, {88, 111}, {144, 167}, {22, 45}, {214, 237}, {210,
233}, {82, 105}, {86, 109}, {146, 169}, {150, 173}, {21, 40}, {31, 32}, {223,
224}, {212, 235}, {159, 160}, {158, 161}, {84, 107}, {95, 96}, {148, 171}, {139,
222}, {39, 122}, {1, 104}, {3, 106}, {5, 108}, {7, 110}, {17, 120}, {21, 124},
{23, 126}, {129, 232}, {131, 234}, {133, 236}, {135, 238}, {42, 65}, {190, 213},
{186, 209}, {174, 197}, {170, 193}, {62, 85}, {46, 69}, {61, 80}, {44, 67},
{188, 211}, {172, 195}, {19, 102}, {48, 71}, {184, 207}, {176, 199}, {56, 79},
{9, 112}, {11, 114}, {13, 116}, {15, 118}, {137, 240}, {50, 73}, {182, 205},
{54, 77}, {181, 200}, {52, 75}, {191, 192}, {63, 64}, {4, 141}, {80, 217}, {70,
207}, {68, 205}, {66, 203}, {64, 201}, {54, 191}, {52, 189}, {50, 187}, {6,
143}, {16, 153}, {18, 155}, {20, 157}, {32, 169}, {34, 171}, {36, 173}, {38,
175}, {48, 185}, {84, 221}, {86, 223}, {96, 233}, {98, 235}, {100, 237}, {8,
145}, {78, 215}, {76, 213}, {74, 211}, {72, 209}, {63, 166}, {61, 164}, {57,
160}, {10, 147}, {12, 149}, {14, 151}, {25, 128}, {27, 130}, {29, 132}, {31,
134}, {40, 177}, {44, 181}, {46, 183}, {89, 192}, {91, 194}, {93, 196}, {95,
198}, {121, 224}, {123, 226}, {125, 228}, {127, 230}, {2, 159}, {22, 179}, {33,
136}, {55, 158}, {53, 156}, {51, 154}, {35, 138}, {37, 140}, {49, 152}, {97,
200}, {101, 204}, {103, 206}, {113, 216}, {115, 218}, {117, 220}, {59, 142},
{24, 161}, {26, 163}, {28, 165}, {30, 167}, {41, 144}, {43, 146}, {45, 148},
{47, 150}, {88, 225}, {90, 227}, {92, 229}, {94, 231}, {105, 208}, {107, 210},
{109, 212}, {111, 214}, {82, 239}, {119, 202}, {99, 182}, {5, 222}, {62, 219},
{7, 224}, {15, 232}, {65, 168}, {83, 186}, {81, 184}, {71, 174}, {69, 172}, {67,
170}, {85, 188}, {87, 190}, {9, 226}, {13, 230}, {106, 129}, {110, 133}, {122,
145}, {126, 149}, {42, 199}, {79, 162}, {1, 238}, {11, 228}, {108, 131}, {124,
147}, {3, 240}, {121, 140}, {112, 135}, {56, 193}, {77, 180}, {75, 178}, {73,
176}, {60, 197}, {58, 195}, {17, 234}, {114, 137}, {19, 236}, {116, 139}, {127,
128} }>;
(II) A more general form is to represent the graph as the orbit of {2, 3}
under the group generated by the following permutations:
a: (2, 238, 20, 104)(3, 135, 19, 127)(4, 112, 18, 230)(5, 9, 17, 13)(6, 226, 16,
116)(7, 123, 15, 139)(8, 120, 14, 222)(10, 234, 12, 108)(11, 131)(21, 231, 141,
111)(22, 208, 160, 214)(23, 105, 159, 237)(24, 82, 158, 100)(25, 239, 157,
103)(26, 216, 156, 206)(27, 113, 155, 229)(28, 90, 154, 92)(29, 227, 153,
115)(30, 204, 152, 218)(31, 101, 151, 221)(32, 98, 150, 84)(33, 235, 149,
107)(34, 212, 148, 210)(35, 109, 147, 233)(36, 86, 146, 96)(37, 223, 145,
119)(38, 220, 144, 202)(39, 117, 143, 225)(40, 94, 142, 88)(41, 201)(42, 198,
60, 64)(43, 95, 59, 87)(44, 72, 58, 190)(45, 209, 57, 213)(46, 186, 56, 76)(47,
83, 55, 99)(48, 80, 54, 182)(49, 217, 53, 205)(50, 194, 52, 68)(51, 91)(61, 191,
181, 71)(62, 168, 200, 174)(63, 65, 199, 197)(66, 176, 196, 166)(67, 73, 195,
189)(69, 187, 193, 75)(70, 164, 192, 178)(74, 172, 188, 170)(77, 183, 185,
79)(78, 180, 184, 162)(81, 161)(85, 169, 97, 173)(89, 177, 93, 165)(102, 128,
240, 134)(106, 136, 236, 126)(110, 124, 232, 138)(114, 132, 228, 130)(118, 140,
224, 122)(125, 129, 137, 133)(163, 215, 179, 207)(167, 203, 175, 219)(171,
211) (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, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20)(21,
102, 23, 104, 25, 106, 27, 108, 29, 110, 31, 112, 33, 114, 35, 116, 37, 118, 39,
120)(22, 103, 24, 105, 26, 107, 28, 109, 30, 111, 32, 113, 34, 115, 36, 117, 38,
119, 40, 101)(41, 202, 43, 204, 45, 206, 47, 208, 49, 210, 51, 212, 53, 214, 55,
216, 57, 218, 59, 220)(42, 203, 44, 205, 46, 207, 48, 209, 50, 211, 52, 213, 54,
215, 56, 217, 58, 219, 60, 201)(61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72,
73, 74, 75, 76, 77, 78, 79, 80)(81, 162, 83, 164, 85, 166, 87, 168, 89, 170, 91,
172, 93, 174, 95, 176, 97, 178, 99, 180)(82, 163, 84, 165, 86, 167, 88, 169, 90,
171, 92, 173, 94, 175, 96, 177, 98, 179, 100, 161)(121, 122, 123, 124, 125, 126,
127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140)(141, 222,
143, 224, 145, 226, 147, 228, 149, 230, 151, 232, 153, 234, 155, 236, 157, 238,
159, 240)(142, 223, 144, 225, 146, 227, 148, 229, 150, 231, 152, 233, 154, 235,
156, 237, 158, 239, 160, 221)(181, 182, 183, 184, 185, 186, 187, 188, 189, 190,
191, 192, 193, 194, 195, 196, 197, 198, 199, 200)
C4[ 240, 41 ]
240
-1 2 104 238 20
-2 1 3 25 159
-3 2 4 106 240
-4 3 5 27 141
-5 222 4 6 108
-6 143 5 7 29
-7 110 224 6 8
-8 145 7 9 31
-9 112 226 8 10
-10 11 33 147 9
-11 12 114 228 10
-12 11 13 35 149
-13 12 14 116 230
-14 13 15 37 151
-15 232 14 16 118
-16 15 17 39 153
-17 234 16 18 120
-18 155 17 19 21
-19 102 236 18 20
-20 1 23 157 19
-21 22 124 18 40
-22 23 45 179 21
-23 22 24 126 20
-24 23 25 47 161
-25 2 24 26 128
-26 25 27 49 163
-27 4 26 28 130
-28 165 27 29 51
-29 132 6 28 30
-30 167 29 31 53
-31 134 8 30 32
-32 33 55 169 31
-33 34 136 10 32
-34 33 35 57 171
-35 12 34 36 138
-36 35 37 59 173
-37 14 36 38 140
-38 37 39 41 175
-39 122 16 38 40
-40 177 39 21 43
-41 144 38 60 42
-42 199 41 43 65
-43 44 146 40 42
-44 45 67 181 43
-45 22 44 46 148
-46 45 47 69 183
-47 24 46 48 150
-48 47 49 71 185
-49 26 48 50 152
-50 187 49 51 73
-51 154 28 50 52
-52 189 51 53 75
-53 156 30 52 54
-54 55 77 191 53
-55 56 158 32 54
-56 55 57 79 193
-57 34 56 58 160
-58 57 59 61 195
-59 36 58 60 142
-60 59 41 63 197
-61 58 80 62 164
-62 61 63 85 219
-63 166 60 62 64
-64 201 63 65 87
-65 66 168 42 64
-66 67 89 203 65
-67 44 66 68 170
-68 67 69 91 205
-69 46 68 70 172
-70 69 71 93 207
-71 48 70 72 174
-72 209 71 73 95
-73 176 50 72 74
-74 211 73 75 97
-75 178 52 74 76
-76 77 99 213 75
-77 78 180 54 76
-78 77 79 81 215
-79 56 78 80 162
-80 79 61 83 217
-81 78 100 82 184
-82 81 83 105 239
-83 80 82 84 186
-84 221 83 85 107
-85 188 62 84 86
-86 223 85 87 109
-87 88 190 64 86
-88 89 111 225 87
-89 66 88 90 192
-90 89 91 113 227
-91 68 90 92 194
-92 91 93 115 229
-93 70 92 94 196
-94 231 93 95 117
-95 198 72 94 96
-96 233 95 97 119
-97 200 74 96 98
-98 99 101 235 97
-99 100 182 76 98
-100 99 81 103 237
-101 102 204 98 120
-102 101 103 125 19
-103 100 102 104 206
-104 1 103 105 127
-105 82 104 106 208
-106 3 105 107 129
-107 210 84 106 108
-108 5 107 109 131
-109 110 212 86 108
-110 111 133 7 109
-111 88 110 112 214
-112 111 113 135 9
-113 90 112 114 216
-114 11 113 115 137
-115 92 114 116 218
-116 13 115 117 139
-117 220 94 116 118
-118 121 15 117 119
-119 202 96 118 120
-120 101 123 17 119
-121 122 224 118 140
-122 121 123 145 39
-123 122 124 226 120
-124 123 125 147 21
-125 102 124 126 228
-126 23 125 127 149
-127 104 126 128 230
-128 25 127 129 151
-129 232 106 128 130
-130 27 129 131 153
-131 132 234 108 130
-132 133 155 29 131
-133 110 132 134 236
-134 133 135 157 31
-135 112 134 136 238
-136 33 135 137 159
-137 114 136 138 240
-138 35 137 139 141
-139 222 116 138 140
-140 121 143 37 139
-141 4 138 160 142
-142 143 165 59 141
-143 144 6 140 142
-144 143 145 167 41
-145 122 144 146 8
-146 145 147 169 43
-147 124 146 148 10
-148 45 147 149 171
-149 12 126 148 150
-150 47 149 151 173
-151 14 128 150 152
-152 49 151 153 175
-153 154 16 130 152
-154 155 177 51 153
-155 132 154 156 18
-156 155 157 179 53
-157 134 156 158 20
-158 55 157 159 161
-159 2 136 158 160
-160 57 159 141 163
-161 24 158 180 162
-162 79 161 163 185
-163 26 160 162 164
-164 165 187 61 163
-165 166 28 142 164
-166 165 167 189 63
-167 144 166 168 30
-168 167 169 191 65
-169 146 168 170 32
-170 67 169 171 193
-171 34 148 170 172
-172 69 171 173 195
-173 36 150 172 174
-174 71 173 175 197
-175 176 38 152 174
-176 177 199 73 175
-177 154 176 178 40
-178 177 179 181 75
-179 22 156 178 180
-180 77 179 161 183
-181 44 178 200 182
-182 99 181 183 205
-183 46 180 182 184
-184 81 183 185 207
-185 48 162 184 186
-186 187 209 83 185
-187 188 50 164 186
-188 187 189 211 85
-189 166 188 190 52
-190 189 191 213 87
-191 168 190 192 54
-192 89 191 193 215
-193 56 170 192 194
-194 91 193 195 217
-195 58 172 194 196
-196 93 195 197 219
-197 198 60 174 196
-198 199 201 95 197
-199 176 198 200 42
-200 199 181 203 97
-201 198 220 202 64
-202 201 203 225 119
-203 66 200 202 204
-204 101 203 205 227
-205 68 182 204 206
-206 103 205 207 229
-207 70 184 206 208
-208 209 231 105 207
-209 210 72 186 208
-210 209 211 233 107
-211 188 210 212 74
-212 211 213 235 109
-213 190 212 214 76
-214 111 213 215 237
-215 78 192 214 216
-216 113 215 217 239
-217 80 194 216 218
-218 221 115 217 219
-219 220 62 196 218
-220 201 223 117 219
-221 222 84 218 240
-222 221 223 5 139
-223 220 222 224 86
-224 121 223 225 7
-225 88 202 224 226
-226 123 225 227 9
-227 90 204 226 228
-228 11 125 227 229
-229 92 206 228 230
-230 231 13 127 229
-231 232 94 208 230
-232 231 233 15 129
-233 210 232 234 96
-234 233 235 17 131
-235 212 234 236 98
-236 133 235 237 19
-237 100 214 236 238
-238 1 135 237 239
-239 82 216 238 240
-240 221 3 137 239
0