Graph forms
for C4 [ 253, 7 ] = MSZ(11,23,4,2)
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On this page are computer-accessible forms for the graph C4[ 253, 7 ] =
MSZ(11,23,4,2).
(I) Following is a form readable by MAGMA:
g:=Graph<253|{ {2, 3}, {252, 253}, {250, 251}, {248, 249}, {246, 247}, {244,
245}, {240, 241}, {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},
{200, 201}, {196, 197}, {194, 195}, {192, 193}, {190, 191}, {188, 189}, {186,
187}, {184, 185}, {182, 183}, {180, 181}, {178, 179}, {174, 175}, {172, 173},
{170, 171}, {168, 169}, {166, 167}, {164, 165}, {162, 163}, {160, 161}, {158,
159}, {156, 157}, {152, 153}, {150, 151}, {148, 149}, {146, 147}, {86, 87}, {84,
85}, {82, 83}, {80, 81}, {78, 79}, {76, 77}, {74, 75}, {72, 73}, {70, 71}, {68,
69}, {64, 65}, {62, 63}, {60, 61}, {58, 59}, {56, 57}, {54, 55}, {52, 53}, {50,
51}, {48, 49}, {46, 47}, {42, 43}, {40, 41}, {38, 39}, {36, 37}, {34, 35}, {32,
33}, {30, 31}, {28, 29}, {26, 27}, {24, 25}, {20, 21}, {18, 19}, {16, 17}, {14,
15}, {12, 13}, {10, 11}, {8, 9}, {6, 7}, {4, 5}, {90, 91}, {92, 93}, {94, 95},
{96, 97}, {98, 99}, {100, 101}, {102, 103}, {104, 105}, {106, 107}, {108, 109},
{112, 113}, {114, 115}, {116, 117}, {118, 119}, {120, 121}, {122, 123}, {124,
125}, {126, 127}, {128, 129}, {130, 131}, {134, 135}, {136, 137}, {138, 139},
{140, 141}, {142, 143}, {144, 145}, {1, 2}, {249, 250}, {245, 246}, {241, 242},
{237, 238}, {233, 234}, {229, 230}, {225, 226}, {221, 222}, {217, 218}, {213,
214}, {205, 206}, {201, 202}, {197, 198}, {193, 194}, {189, 190}, {185, 186},
{181, 182}, {177, 178}, {173, 174}, {169, 170}, {161, 162}, {157, 158}, {153,
154}, {149, 150}, {145, 146}, {89, 90}, {85, 86}, {81, 82}, {73, 74}, {69, 70},
{65, 66}, {61, 62}, {57, 58}, {53, 54}, {49, 50}, {45, 46}, {41, 42}, {37, 38},
{29, 30}, {25, 26}, {21, 22}, {17, 18}, {13, 14}, {9, 10}, {5, 6}, {93, 94},
{97, 98}, {101, 102}, {105, 106}, {109, 110}, {113, 114}, {117, 118}, {125,
126}, {129, 130}, {133, 134}, {137, 138}, {141, 142}, {11, 15}, {242, 246},
{209, 213}, {187, 191}, {176, 180}, {154, 158}, {88, 92}, {66, 70}, {33, 37},
{99, 103}, {121, 125}, {3, 4}, {251, 252}, {243, 244}, {235, 236}, {227, 228},
{219, 220}, {211, 212}, {203, 204}, {195, 196}, {179, 180}, {171, 172}, {163,
164}, {155, 156}, {147, 148}, {83, 84}, {75, 76}, {67, 68}, {59, 60}, {51, 52},
{43, 44}, {35, 36}, {27, 28}, {19, 20}, {91, 92}, {107, 108}, {115, 116}, {123,
124}, {131, 132}, {139, 140}, {1, 11}, {177, 187}, {100, 110}, {133, 143}, {144,
154}, {22, 26}, {231, 235}, {198, 202}, {165, 169}, {55, 59}, {132, 136}, {34,
44}, {243, 253}, {210, 220}, {67, 77}, {7, 8}, {247, 248}, {215, 216}, {199,
200}, {183, 184}, {167, 168}, {151, 152}, {87, 88}, {71, 72}, {39, 40}, {23,
24}, {103, 104}, {119, 120}, {135, 136}, {78, 88}, {199, 209}, {166, 176}, {111,
121}, {1, 27}, {232, 242}, {45, 55}, {12, 22}, {96, 122}, {100, 126}, {129,
155}, {133, 159}, {44, 48}, {77, 81}, {110, 114}, {143, 147}, {34, 60}, {195,
221}, {162, 188}, {67, 93}, {15, 16}, {239, 240}, {207, 208}, {175, 176}, {79,
80}, {47, 48}, {111, 112}, {23, 49}, {206, 232}, {199, 225}, {151, 177}, {78,
104}, {30, 56}, {8, 34}, {221, 247}, {217, 243}, {12, 38}, {89, 115}, {140,
166}, {74, 100}, {155, 181}, {2, 50}, {200, 248}, {79, 127}, {68, 116}, {13,
61}, {134, 182}, {76, 127}, {65, 116}, {131, 182}, {23, 33}, {10, 61}, {85,
111}, {221, 231}, {89, 99}, {144, 170}, {64, 123}, {220, 224}, {197, 248}, {19,
45}, {210, 236}, {155, 165}, {31, 32}, {223, 224}, {159, 160}, {95, 96}, {130,
189}, {31, 90}, {53, 112}, {141, 200}, {174, 233}, {52, 125}, {162, 235}, {129,
202}, {152, 211}, {9, 68}, {185, 244}, {175, 226}, {19, 92}, {42, 101}, {142,
193}, {24, 72}, {189, 237}, {178, 226}, {156, 204}, {145, 193}, {57, 105}, {153,
204}, {186, 237}, {8, 81}, {140, 213}, {20, 79}, {173, 246}, {41, 114}, {3, 95},
{21, 72}, {54, 105}, {14, 106}, {157, 249}, {135, 227}, {63, 89}, {166, 192},
{16, 119}, {5, 108}, {41, 67}, {188, 214}, {184, 210}, {173, 199}, {56, 82},
{45, 71}, {132, 238}, {25, 117}, {148, 251}, {35, 83}, {167, 215}, {46, 94},
{32, 83}, {164, 215}, {43, 94}, {143, 249}, {151, 224}, {30, 103}, {137, 240},
{52, 78}, {188, 198}, {177, 203}, {56, 66}, {146, 238}, {163, 222}, {11, 117},
{63, 64}, {191, 192}, {3, 131}, {80, 208}, {69, 197}, {58, 186}, {47, 175}, {36,
164}, {25, 153}, {14, 142}, {91, 219}, {102, 230}, {113, 241}, {124, 252}, {43,
168}, {87, 212}, {54, 179}, {76, 201}, {21, 146}, {109, 234}, {10, 135}, {120,
245}, {40, 187}, {73, 220}, {9, 159}, {64, 214}, {55, 161}, {22, 128}, {97,
247}, {106, 253}, {27, 130}, {93, 196}, {88, 194}, {121, 227}, {126, 229}, {7,
154}, {60, 163}, {18, 179}, {84, 245}, {29, 190}, {73, 234}, {36, 128}, {47,
139}, {102, 194}, {124, 216}, {104, 207}, {49, 152}, {115, 218}, {31, 181}, {75,
225}, {33, 139}, {38, 141}, {58, 150}, {29, 176}, {95, 242}, {99, 205}, {7,
168}, {84, 231}, {110, 216}, {18, 165}, {63, 136}, {44, 150}, {86, 236}, {4,
184}, {70, 250}, {113, 205}, {32, 157}, {98, 223}, {20, 170}, {13, 207}, {57,
251}, {24, 218}, {119, 178}, {2, 196}, {35, 229}, {86, 145}, {96, 169}, {118,
191}, {17, 219}, {85, 158}, {108, 167}, {15, 195}, {75, 134}, {109, 160}, {50,
252}, {17, 222}, {90, 138}, {112, 160}, {123, 171}, {39, 244}, {120, 171}, {26,
206}, {59, 239}, {48, 228}, {6, 211}, {6, 208}, {39, 241}, {74, 147}, {87, 138},
{46, 240}, {107, 180}, {40, 201}, {62, 223}, {12, 239}, {16, 243}, {69, 161},
{1, 228}, {111, 137}, {118, 144}, {51, 212}, {71, 174}, {42, 192}, {82, 185},
{91, 183}, {5, 232}, {23, 250}, {66, 172}, {107, 133}, {122, 148}, {62, 209},
{101, 149}, {28, 233}, {51, 198}, {98, 149}, {4, 253}, {28, 230}, {77, 183},
{37, 217}, {80, 172}, {97, 156}, {53, 203}, {122, 132}, {65, 190}, {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: (1, 2, 196, 197, 248, 200, 199, 225, 226, 227, 228)(3, 93, 69, 249, 141, 209,
224, 178, 121, 229, 27)(4, 92, 161, 157, 38, 208, 220, 179, 111, 35, 26)(5, 91,
55, 158, 37, 207, 210, 18, 112, 83, 22)(6, 219, 54, 85, 36, 206, 184, 19, 160,
32, 12)(7, 218, 105, 86, 164, 205, 185, 20, 109, 31, 239)(8, 24, 106, 87, 163,
204, 244, 79, 234, 181, 240)(9, 23, 14, 212, 222, 203, 245, 127, 233, 182,
46)(10, 49, 15, 51, 221, 202, 246, 76, 174, 134, 47)(11, 50, 195, 198, 247, 201,
173, 75, 175, 135, 48)(13, 211, 17, 53, 84, 128, 232, 183, 45, 159, 33)(16, 52,
231, 129, 242, 77, 71, 133, 139, 61, 152)(21, 108, 90, 59, 154, 217, 104, 236,
165, 113, 82)(25, 253, 88, 162, 156, 39, 80, 73, 180, 137, 34)(28, 131, 94, 68,
250, 142, 213, 223, 177, 120, 126)(29, 132, 43, 116, 251, 193, 214, 98, 187,
171, 100)(30, 238, 168, 115, 57, 145, 215, 99, 186, 170, 110)(40, 172, 74, 176,
136, 44, 117, 252, 194, 188, 97)(41, 66, 147, 166, 63, 150, 118, 124, 102, 189,
96)(42, 65, 148, 192, 64, 149, 191, 123, 101, 190, 122)(56, 146, 167, 89, 58,
144, 216, 103, 237, 169, 114)(60, 153, 243, 78, 235, 155, 241, 81, 72, 107,
138)(62, 151, 119, 125, 230, 130, 95, 67, 70, 143, 140) (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, 11)(3, 117)(4, 116)(5, 65)(6, 64)(7, 123)(8, 124)(9, 252)(10, 50)(12,
202)(13, 198)(14, 197)(15, 196)(16, 93)(17, 92)(18, 19)(20, 165)(21, 155)(22,
129)(23, 134)(24, 182)(25, 131)(26, 130)(29, 233)(30, 234)(31, 73)(32, 74)(33,
75)(34, 125)(35, 126)(36, 127)(37, 76)(38, 201)(39, 40)(41, 244)(42, 245)(43,
120)(44, 121)(45, 179)(46, 178)(47, 226)(48, 227)(49, 135)(51, 61)(52, 60)(53,
59)(54, 55)(56, 109)(57, 160)(58, 112)(62, 212)(63, 211)(66, 108)(67, 243)(68,
253)(69, 106)(70, 107)(71, 180)(72, 181)(77, 217)(78, 163)(79, 164)(80, 215)(81,
216)(82, 110)(83, 100)(84, 101)(85, 149)(86, 98)(87, 223)(88, 222)(89, 210)(90,
220)(91, 219)(94, 119)(95, 118)(96, 144)(97, 145)(99, 236)(102, 231)(103,
235)(104, 162)(105, 161)(111, 150)(113, 186)(114, 185)(115, 184)(122, 154)(132,
153)(133, 250)(136, 152)(137, 151)(138, 224)(139, 225)(140, 199)(141, 200)(142,
248)(143, 249)(146, 156)(147, 157)(148, 158)(159, 251)(166, 173)(167, 172)(168,
171)(169, 170)(174, 176)(177, 240)(183, 218)(187, 241)(188, 207)(189, 206)(190,
232)(191, 242)(192, 246)(193, 247)(194, 221)(203, 239)(204, 238)(205, 237)(208,
214)(209, 213)
c: (2, 228, 11)(3, 229, 117)(4, 126, 118)(5, 127, 191)(6, 76, 192)(7, 77, 42)(8,
67, 43)(9, 93, 44)(10, 196, 48)(12, 188, 174)(13, 198, 175)(14, 51, 226)(15, 50,
227)(16, 252, 121)(17, 251, 111)(18, 57, 112)(19, 58, 160)(20, 186, 109)(21,
237, 234)(22, 189, 233)(23, 136, 221)(24, 132, 231)(25, 131, 230)(26, 130,
28)(29, 206, 129)(30, 205, 155)(31, 99, 156)(32, 89, 97)(33, 63, 247)(34, 68,
94)(35, 116, 95)(36, 65, 242)(37, 64, 246)(38, 214, 173)(39, 215, 172)(40, 167,
80)(41, 168, 81)(45, 59, 161)(46, 60, 69)(47, 61, 197)(49, 135, 195)(52, 178,
106)(53, 179, 105)(56, 113, 165)(62, 248, 139)(66, 241, 164)(70, 240, 163)(71,
239, 162)(72, 238, 235)(73, 146, 236)(74, 145, 210)(75, 193, 211)(78, 177,
107)(79, 187, 108)(82, 114, 169)(83, 115, 96)(84, 218, 122)(85, 219, 148)(86,
220, 147)(87, 224, 143)(88, 151, 133)(90, 98, 157)(91, 149, 158)(92, 150,
159)(100, 144, 184)(101, 154, 183)(102, 153, 182)(103, 204, 181)(104, 203,
180)(110, 170, 185)(119, 253, 125)(120, 243, 124)(123, 245, 217)(128, 190,
232)(134, 194, 152)(137, 222, 250)(138, 223, 249)(140, 209, 200)(141, 213,
199)(142, 212, 225)(166, 208, 201)(171, 244, 216)(176, 207, 202)
d: (2, 11)(3, 10)(4, 9)(5, 8)(6, 7)(12, 46)(13, 94)(14, 93)(15, 196)(16,
197)(17, 248)(18, 200)(19, 141)(20, 140)(21, 139)(22, 47)(23, 24)(25, 49)(26,
48)(27, 228)(28, 229)(29, 126)(30, 100)(31, 74)(32, 73)(33, 72)(34, 232)(35,
233)(36, 174)(37, 71)(38, 45)(39, 55)(40, 54)(41, 105)(42, 104)(43, 207)(44,
206)(50, 117)(51, 118)(52, 191)(53, 187)(56, 110)(57, 114)(58, 113)(59, 241)(60,
242)(61, 95)(62, 96)(63, 122)(64, 123)(65, 124)(66, 216)(67, 106)(68, 253)(69,
243)(70, 217)(75, 181)(76, 180)(77, 107)(78, 192)(79, 166)(80, 167)(81, 108)(82,
109)(83, 234)(84, 235)(85, 236)(87, 145)(88, 193)(89, 148)(90, 147)(91, 143)(92,
142)(97, 223)(99, 149)(101, 103)(111, 237)(112, 186)(115, 251)(116, 252)(119,
198)(120, 188)(121, 189)(125, 190)(127, 176)(128, 175)(129, 226)(130, 227)(131,
135)(132, 136)(133, 183)(134, 182)(137, 238)(138, 146)(144, 212)(150, 205)(151,
204)(152, 153)(154, 211)(155, 225)(156, 224)(157, 220)(158, 210)(159, 184)(160,
185)(161, 244)(162, 245)(163, 246)(164, 173)(165, 199)(168, 208)(169, 209)(170,
213)(171, 214)(172, 215)(177, 203)(178, 202)(179, 201)(218, 250)(219, 249)(222,
247)(239, 240)
C4[ 253, 7 ]
253
-1 11 2 27 228
-2 1 3 50 196
-3 2 4 95 131
-4 253 3 5 184
-5 232 4 6 108
-6 211 5 7 208
-7 154 168 6 8
-8 34 81 7 9
-9 68 159 8 10
-10 11 135 61 9
-11 1 15 117 10
-12 22 13 38 239
-13 12 14 61 207
-14 13 15 106 142
-15 11 14 16 195
-16 243 15 17 119
-17 222 16 18 219
-18 165 179 17 19
-19 45 92 18 20
-20 79 170 19 21
-21 22 146 72 20
-22 12 26 128 21
-23 33 24 49 250
-24 23 25 72 218
-25 24 26 117 153
-26 22 25 27 206
-27 1 26 28 130
-28 233 27 29 230
-29 176 190 28 30
-30 56 103 29 31
-31 90 181 30 32
-32 33 157 83 31
-33 23 37 139 32
-34 44 35 60 8
-35 34 36 83 229
-36 35 37 128 164
-37 33 36 38 217
-38 12 37 39 141
-39 244 38 40 241
-40 187 201 39 41
-41 67 114 40 42
-42 101 192 41 43
-43 44 168 94 42
-44 34 48 150 43
-45 55 46 71 19
-46 45 47 94 240
-47 46 48 139 175
-48 44 47 49 228
-49 23 48 50 152
-50 2 49 51 252
-51 198 212 50 52
-52 78 125 51 53
-53 112 203 52 54
-54 55 179 105 53
-55 45 59 161 54
-56 66 57 82 30
-57 56 58 105 251
-58 57 59 150 186
-59 55 58 60 239
-60 34 59 61 163
-61 13 60 62 10
-62 209 223 61 63
-63 89 136 62 64
-64 123 214 63 65
-65 66 190 116 64
-66 56 70 172 65
-67 77 68 93 41
-68 67 69 116 9
-69 68 70 161 197
-70 66 69 71 250
-71 45 70 72 174
-72 24 71 73 21
-73 220 234 72 74
-74 100 147 73 75
-75 134 225 74 76
-76 77 201 127 75
-77 67 81 183 76
-78 88 79 104 52
-79 78 80 127 20
-80 79 81 172 208
-81 77 80 82 8
-82 56 81 83 185
-83 35 82 84 32
-84 231 245 83 85
-85 111 158 84 86
-86 145 236 85 87
-87 88 212 138 86
-88 78 92 194 87
-89 99 90 115 63
-90 89 91 138 31
-91 90 92 183 219
-92 88 91 93 19
-93 67 92 94 196
-94 46 93 95 43
-95 242 3 94 96
-96 122 169 95 97
-97 156 247 96 98
-98 99 223 149 97
-99 89 103 205 98
-100 110 101 126 74
-101 100 102 149 42
-102 101 103 194 230
-103 99 102 104 30
-104 78 103 105 207
-105 57 104 106 54
-106 253 14 105 107
-107 133 180 106 108
-108 167 5 107 109
-109 110 234 160 108
-110 100 114 216 109
-111 121 112 137 85
-112 111 113 160 53
-113 112 114 205 241
-114 110 113 115 41
-115 89 114 116 218
-116 68 115 117 65
-117 11 25 116 118
-118 144 191 117 119
-119 178 16 118 120
-120 121 245 171 119
-121 111 125 227 120
-122 132 123 148 96
-123 122 124 171 64
-124 123 125 216 252
-125 121 124 126 52
-126 100 125 127 229
-127 79 126 128 76
-128 22 36 127 129
-129 155 202 128 130
-130 189 27 129 131
-131 132 3 182 130
-132 122 136 238 131
-133 143 134 159 107
-134 133 135 182 75
-135 134 136 227 10
-136 132 135 137 63
-137 111 136 138 240
-138 90 137 139 87
-139 33 47 138 140
-140 166 213 139 141
-141 200 38 140 142
-142 143 14 193 141
-143 133 147 249 142
-144 154 145 170 118
-145 144 146 193 86
-146 145 147 238 21
-147 143 146 148 74
-148 122 147 149 251
-149 101 148 150 98
-150 44 58 149 151
-151 177 224 150 152
-152 211 49 151 153
-153 154 25 204 152
-154 144 158 7 153
-155 165 156 181 129
-156 155 157 204 97
-157 156 158 249 32
-158 154 157 159 85
-159 133 158 160 9
-160 112 159 161 109
-161 55 69 160 162
-162 188 235 161 163
-163 222 60 162 164
-164 165 36 215 163
-165 155 169 18 164
-166 176 167 192 140
-167 166 168 215 108
-168 167 169 7 43
-169 165 168 170 96
-170 144 169 171 20
-171 123 170 172 120
-172 66 80 171 173
-173 199 246 172 174
-174 233 71 173 175
-175 176 47 226 174
-176 166 180 29 175
-177 187 178 203 151
-178 177 179 226 119
-179 178 180 18 54
-180 176 179 181 107
-181 155 180 182 31
-182 134 181 183 131
-183 77 91 182 184
-184 210 4 183 185
-185 244 82 184 186
-186 187 58 237 185
-187 177 191 40 186
-188 198 189 214 162
-189 188 190 237 130
-190 189 191 29 65
-191 187 190 192 118
-192 166 191 193 42
-193 145 192 194 142
-194 88 102 193 195
-195 221 15 194 196
-196 2 93 195 197
-197 198 69 248 196
-198 188 202 51 197
-199 209 200 225 173
-200 199 201 248 141
-201 200 202 40 76
-202 198 201 203 129
-203 177 202 204 53
-204 156 203 205 153
-205 99 113 204 206
-206 232 26 205 207
-207 13 104 206 208
-208 209 80 6 207
-209 199 213 62 208
-210 220 211 236 184
-211 210 212 6 152
-212 211 213 51 87
-213 209 212 214 140
-214 188 213 215 64
-215 167 214 216 164
-216 110 124 215 217
-217 243 37 216 218
-218 24 115 217 219
-219 220 91 17 218
-220 210 224 73 219
-221 231 222 247 195
-222 221 223 17 163
-223 222 224 62 98
-224 220 223 225 151
-225 199 224 226 75
-226 178 225 227 175
-227 121 135 226 228
-228 1 48 227 229
-229 35 126 228 230
-230 231 102 28 229
-231 221 235 84 230
-232 242 233 5 206
-233 232 234 28 174
-234 233 235 73 109
-235 231 234 236 162
-236 210 235 237 86
-237 189 236 238 186
-238 132 146 237 239
-239 12 59 238 240
-240 46 137 239 241
-241 242 113 39 240
-242 232 246 95 241
-243 253 244 16 217
-244 243 245 39 185
-245 244 246 84 120
-246 242 245 247 173
-247 221 246 248 97
-248 200 247 249 197
-249 143 157 248 250
-250 23 70 249 251
-251 57 148 250 252
-252 253 124 50 251
-253 243 4 106 252
0