Graph forms
for C4 [ 270, 7 ] = PS(18,15;4)
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On this page are computer-accessible forms for the graph C4[ 270, 7 ] =
PS(18,15;4).
(I) Following is a form readable by MAGMA:
g:=Graph<270|{ {45, 46}, {105, 106}, {165, 166}, {225, 226}, {27, 31}, {240,
244}, {120, 124}, {90, 94}, {89, 93}, {88, 92}, {57, 61}, {58, 62}, {59, 63},
{147, 151}, {177, 181}, {178, 182}, {179, 183}, {208, 212}, {209, 213}, {210,
214}, {75, 76}, {195, 196}, {20, 31}, {240, 251}, {116, 127}, {112, 123}, {84,
95}, {80, 91}, {52, 63}, {144, 155}, {148, 159}, {176, 187}, {180, 191}, {208,
219}, {87, 91}, {119, 123}, {118, 122}, {117, 121}, {148, 152}, {149, 153},
{150, 154}, {180, 184}, {51, 62}, {115, 126}, {113, 124}, {83, 94}, {81, 92},
{145, 156}, {147, 158}, {177, 188}, {179, 190}, {209, 220}, {32, 46}, {129,
143}, {128, 142}, {97, 111}, {96, 110}, {33, 47}, {64, 78}, {65, 79}, {160,
174}, {161, 175}, {192, 206}, {193, 207}, {224, 238}, {225, 239}, {50, 61},
{114, 125}, {82, 93}, {135, 136}, {146, 157}, {178, 189}, {210, 221}, {1, 17},
{133, 149}, {132, 148}, {131, 147}, {130, 146}, {129, 145}, {128, 144}, {104,
120}, {103, 119}, {102, 118}, {101, 117}, {100, 116}, {99, 115}, {98, 114}, {97,
113}, {96, 112}, {74, 90}, {73, 89}, {2, 18}, {3, 19}, {4, 20}, {5, 21}, {6,
22}, {7, 23}, {8, 24}, {9, 25}, {10, 26}, {11, 27}, {12, 28}, {13, 29}, {14,
30}, {32, 48}, {33, 49}, {34, 50}, {35, 51}, {36, 52}, {37, 53}, {38, 54}, {39,
55}, {40, 56}, {41, 57}, {42, 58}, {43, 59}, {44, 60}, {64, 80}, {65, 81}, {66,
82}, {67, 83}, {68, 84}, {69, 85}, {70, 86}, {71, 87}, {72, 88}, {134, 150},
{160, 176}, {161, 177}, {162, 178}, {163, 179}, {164, 180}, {192, 208}, {193,
209}, {194, 210}, {224, 240}, {2, 16}, {134, 148}, {131, 145}, {130, 144}, {103,
117}, {102, 116}, {99, 113}, {98, 112}, {75, 89}, {74, 88}, {3, 17}, {6, 20},
{7, 21}, {10, 24}, {11, 25}, {14, 28}, {15, 29}, {34, 48}, {35, 49}, {38, 52},
{39, 53}, {42, 56}, {43, 57}, {66, 80}, {67, 81}, {70, 84}, {71, 85}, {135,
149}, {162, 176}, {163, 177}, {194, 208}, {195, 209}, {76, 95}, {236, 255},
{232, 251}, {228, 247}, {108, 127}, {136, 155}, {140, 159}, {168, 187}, {172,
191}, {196, 215}, {200, 219}, {204, 223}, {107, 126}, {239, 250}, {237, 248},
{235, 254}, {233, 252}, {231, 242}, {227, 246}, {111, 122}, {137, 156}, {139,
158}, {141, 152}, {143, 154}, {169, 188}, {171, 190}, {173, 184}, {175, 186},
{201, 220}, {203, 222}, {205, 216}, {207, 218}, {4, 18}, {133, 147}, {132, 146},
{101, 115}, {100, 114}, {5, 19}, {12, 26}, {13, 27}, {36, 50}, {37, 51}, {44,
58}, {45, 59}, {68, 82}, {69, 83}, {164, 178}, {165, 179}, {106, 125}, {238,
249}, {234, 253}, {230, 241}, {110, 121}, {138, 157}, {142, 153}, {170, 189},
{174, 185}, {202, 221}, {206, 217}, {226, 245}, {196, 222}, {229, 255}, {228,
254}, {197, 223}, {140, 151}, {236, 247}, {232, 243}, {172, 183}, {200, 211},
{204, 215}, {207, 211}, {239, 243}, {238, 242}, {237, 241}, {167, 186}, {235,
246}, {233, 244}, {231, 250}, {229, 248}, {171, 182}, {197, 216}, {199, 218},
{201, 212}, {203, 214}, {8, 22}, {227, 253}, {105, 119}, {104, 118}, {9, 23},
{40, 54}, {41, 55}, {72, 86}, {73, 87}, {226, 252}, {1, 30}, {234, 245}, {230,
249}, {15, 16}, {166, 185}, {170, 181}, {198, 217}, {202, 213}, {31, 60}, {91,
120}, {151, 180}, {211, 240}, {78, 104}, {79, 105}, {198, 224}, {199, 225}, {76,
102}, {77, 103}, {136, 162}, {137, 163}, {77, 96}, {79, 98}, {141, 160}, {143,
162}, {205, 224}, {138, 164}, {139, 165}, {78, 97}, {142, 161}, {206, 225}, {31,
47}, {95, 111}, {94, 110}, {93, 109}, {92, 108}, {91, 107}, {151, 167}, {152,
168}, {153, 169}, {154, 170}, {155, 171}, {156, 172}, {157, 173}, {158, 174},
{159, 175}, {211, 227}, {212, 228}, {213, 229}, {214, 230}, {215, 231}, {216,
232}, {217, 233}, {218, 234}, {219, 235}, {220, 236}, {221, 237}, {222, 238},
{223, 239}, {94, 108}, {95, 109}, {154, 168}, {155, 169}, {158, 172}, {159,
173}, {214, 228}, {215, 229}, {218, 232}, {219, 233}, {222, 236}, {223, 237},
{16, 35}, {84, 103}, {80, 99}, {20, 39}, {24, 43}, {144, 163}, {17, 36}, {87,
98}, {85, 96}, {83, 102}, {81, 100}, {19, 38}, {21, 32}, {23, 34}, {25, 44},
{29, 40}, {145, 164}, {149, 160}, {92, 106}, {93, 107}, {156, 170}, {157, 171},
{212, 226}, {213, 227}, {220, 234}, {221, 235}, {18, 37}, {86, 97}, {82, 101},
{22, 33}, {26, 45}, {30, 41}, {146, 165}, {150, 161}, {16, 42}, {17, 43}, {24,
35}, {88, 99}, {28, 39}, {28, 32}, {29, 33}, {30, 34}, {21, 40}, {89, 100}, {85,
104}, {23, 42}, {25, 36}, {27, 38}, {18, 44}, {19, 45}, {152, 166}, {153, 167},
{216, 230}, {217, 231}, {22, 41}, {90, 101}, {86, 105}, {26, 37}, {46, 72}, {47,
73}, {166, 192}, {167, 193}, {61, 90}, {181, 210}, {168, 194}, {169, 195}, {47,
66}, {173, 192}, {175, 194}, {46, 65}, {174, 193}, {61, 77}, {62, 78}, {63, 79},
{181, 197}, {182, 198}, {183, 199}, {184, 200}, {185, 201}, {186, 202}, {187,
203}, {188, 204}, {189, 205}, {190, 206}, {191, 207}, {62, 76}, {63, 77}, {182,
196}, {183, 197}, {186, 200}, {187, 201}, {190, 204}, {191, 205}, {48, 67}, {52,
71}, {56, 75}, {176, 195}, {49, 68}, {51, 70}, {53, 64}, {55, 66}, {188, 202},
{189, 203}, {50, 69}, {54, 65}, {48, 74}, {49, 75}, {56, 67}, {60, 71}, {60,
64}, {53, 72}, {55, 74}, {57, 68}, {59, 70}, {184, 198}, {185, 199}, {54, 73},
{58, 69}, {108, 134}, {109, 135}, {109, 128}, {111, 130}, {106, 132}, {107,
133}, {110, 129}, {121, 150}, {121, 137}, {127, 143}, {126, 142}, {125, 141},
{124, 140}, {123, 139}, {122, 138}, {122, 136}, {127, 141}, {126, 140}, {123,
137}, {112, 131}, {116, 135}, {113, 132}, {119, 130}, {117, 128}, {115, 134},
{124, 138}, {125, 139}, {114, 133}, {118, 129}, {120, 131}, {4, 263}, {8, 267},
{1, 260}, {3, 262}, {5, 256}, {7, 258}, {9, 268}, {11, 270}, {13, 264}, {15,
266}, {2, 261}, {6, 257}, {10, 269}, {14, 265}, {1, 267}, {4, 270}, {8, 259},
{12, 263}, {12, 256}, {13, 257}, {14, 258}, {15, 259}, {5, 264}, {7, 266}, {9,
260}, {11, 262}, {2, 268}, {3, 269}, {6, 265}, {10, 261}, {241, 257}, {254,
270}, {253, 269}, {252, 268}, {251, 267}, {250, 266}, {249, 265}, {248, 264},
{247, 263}, {246, 262}, {245, 261}, {244, 260}, {243, 259}, {242, 258}, {242,
256}, {255, 269}, {254, 268}, {251, 265}, {250, 264}, {247, 261}, {246, 260},
{243, 257}, {244, 258}, {253, 267}, {252, 266}, {245, 259}, {248, 262}, {249,
263}, {241, 270}, {255, 256} }>;
(II) A more general form is to represent the graph as the orbit of {45, 46}
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, 223, 224,
225)(226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239,
240)(241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254,
255)(256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269,
270) (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)(4, 13)(7, 10)(8, 14)(12, 15)(16, 256)(17, 260)(18, 264)(19,
268)(20, 257)(21, 261)(22, 265)(23, 269)(24, 258)(25, 262)(26, 266)(27, 270)(28,
259)(29, 263)(30, 267)(31, 241)(32, 245)(33, 249)(34, 253)(35, 242)(36, 246)(37,
250)(38, 254)(39, 243)(40, 247)(41, 251)(42, 255)(43, 244)(44, 248)(45, 252)(46,
226)(47, 230)(48, 234)(49, 238)(50, 227)(51, 231)(52, 235)(53, 239)(54, 228)(55,
232)(56, 236)(57, 240)(58, 229)(59, 233)(60, 237)(61, 211)(62, 215)(63, 219)(64,
223)(65, 212)(66, 216)(67, 220)(68, 224)(69, 213)(70, 217)(71, 221)(72, 225)(73,
214)(74, 218)(75, 222)(76, 196)(77, 200)(78, 204)(79, 208)(80, 197)(81, 201)(82,
205)(83, 209)(84, 198)(85, 202)(86, 206)(87, 210)(88, 199)(89, 203)(90, 207)(91,
181)(92, 185)(93, 189)(94, 193)(95, 182)(96, 186)(97, 190)(98, 194)(99,
183)(100, 187)(101, 191)(102, 195)(103, 184)(104, 188)(105, 192)(106, 166)(107,
170)(108, 174)(109, 178)(110, 167)(111, 171)(112, 175)(113, 179)(114, 168)(115,
172)(116, 176)(117, 180)(118, 169)(119, 173)(120, 177)(121, 151)(122, 155)(123,
159)(124, 163)(125, 152)(126, 156)(127, 160)(128, 164)(129, 153)(130, 157)(131,
161)(132, 165)(133, 154)(134, 158)(135, 162)(137, 140)(138, 144)(139, 148)(142,
145)(143, 149)(147, 150)
c: (2, 15)(3, 14)(4, 13)(5, 12)(6, 11)(7, 10)(8, 9)(17, 30)(18, 29)(19, 28)(20,
27)(21, 26)(22, 25)(23, 24)(32, 45)(33, 44)(34, 43)(35, 42)(36, 41)(37, 40)(38,
39)(47, 60)(48, 59)(49, 58)(50, 57)(51, 56)(52, 55)(53, 54)(62, 75)(63, 74)(64,
73)(65, 72)(66, 71)(67, 70)(68, 69)(77, 90)(78, 89)(79, 88)(80, 87)(81, 86)(82,
85)(83, 84)(92, 105)(93, 104)(94, 103)(95, 102)(96, 101)(97, 100)(98, 99)(107,
120)(108, 119)(109, 118)(110, 117)(111, 116)(112, 115)(113, 114)(122, 135)(123,
134)(124, 133)(125, 132)(126, 131)(127, 130)(128, 129)(137, 150)(138, 149)(139,
148)(140, 147)(141, 146)(142, 145)(143, 144)(152, 165)(153, 164)(154, 163)(155,
162)(156, 161)(157, 160)(158, 159)(167, 180)(168, 179)(169, 178)(170, 177)(171,
176)(172, 175)(173, 174)(182, 195)(183, 194)(184, 193)(185, 192)(186, 191)(187,
190)(188, 189)(197, 210)(198, 209)(199, 208)(200, 207)(201, 206)(202, 205)(203,
204)(212, 225)(213, 224)(214, 223)(215, 222)(216, 221)(217, 220)(218, 219)(227,
240)(228, 239)(229, 238)(230, 237)(231, 236)(232, 235)(233, 234)(242, 255)(243,
254)(244, 253)(245, 252)(246, 251)(247, 250)(248, 249)(257, 270)(258, 269)(259,
268)(260, 267)(261, 266)(262, 265)(263, 264)
d: (1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11,
26)(12, 27)(13, 28)(14, 29)(15, 30)(31, 256)(32, 257)(33, 258)(34, 259)(35,
260)(36, 261)(37, 262)(38, 263)(39, 264)(40, 265)(41, 266)(42, 267)(43, 268)(44,
269)(45, 270)(46, 241)(47, 242)(48, 243)(49, 244)(50, 245)(51, 246)(52, 247)(53,
248)(54, 249)(55, 250)(56, 251)(57, 252)(58, 253)(59, 254)(60, 255)(61, 226)(62,
227)(63, 228)(64, 229)(65, 230)(66, 231)(67, 232)(68, 233)(69, 234)(70, 235)(71,
236)(72, 237)(73, 238)(74, 239)(75, 240)(76, 211)(77, 212)(78, 213)(79, 214)(80,
215)(81, 216)(82, 217)(83, 218)(84, 219)(85, 220)(86, 221)(87, 222)(88, 223)(89,
224)(90, 225)(91, 196)(92, 197)(93, 198)(94, 199)(95, 200)(96, 201)(97, 202)(98,
203)(99, 204)(100, 205)(101, 206)(102, 207)(103, 208)(104, 209)(105, 210)(106,
181)(107, 182)(108, 183)(109, 184)(110, 185)(111, 186)(112, 187)(113, 188)(114,
189)(115, 190)(116, 191)(117, 192)(118, 193)(119, 194)(120, 195)(121, 166)(122,
167)(123, 168)(124, 169)(125, 170)(126, 171)(127, 172)(128, 173)(129, 174)(130,
175)(131, 176)(132, 177)(133, 178)(134, 179)(135, 180)(136, 151)(137, 152)(138,
153)(139, 154)(140, 155)(141, 156)(142, 157)(143, 158)(144, 159)(145, 160)(146,
161)(147, 162)(148, 163)(149, 164)(150, 165)
C4[ 270, 7 ]
270
-1 267 17 260 30
-2 268 16 18 261
-3 269 17 19 262
-4 270 18 20 263
-5 264 256 19 21
-6 22 265 257 20
-7 23 266 258 21
-8 22 24 267 259
-9 23 25 268 260
-10 24 26 269 261
-11 25 27 270 262
-12 256 26 28 263
-13 264 257 27 29
-14 265 258 28 30
-15 266 16 259 29
-16 2 35 15 42
-17 1 3 36 43
-18 44 2 4 37
-19 45 3 5 38
-20 4 6 39 31
-21 5 7 40 32
-22 33 6 8 41
-23 34 7 9 42
-24 35 8 10 43
-25 11 44 36 9
-26 12 45 37 10
-27 11 13 38 31
-28 12 14 39 32
-29 33 13 15 40
-30 1 34 14 41
-31 47 27 60 20
-32 46 48 28 21
-33 22 47 49 29
-34 23 48 50 30
-35 24 16 49 51
-36 25 17 50 52
-37 26 18 51 53
-38 27 19 52 54
-39 55 28 20 53
-40 56 29 21 54
-41 22 55 57 30
-42 23 56 58 16
-43 24 57 59 17
-44 25 58 60 18
-45 46 26 59 19
-46 45 72 32 65
-47 33 66 73 31
-48 34 67 74 32
-49 33 35 68 75
-50 34 36 69 61
-51 35 37 70 62
-52 36 38 71 63
-53 37 39 72 64
-54 38 40 73 65
-55 66 39 41 74
-56 67 40 42 75
-57 68 61 41 43
-58 44 69 62 42
-59 45 70 63 43
-60 44 71 31 64
-61 77 57 90 50
-62 78 58 51 76
-63 77 79 59 52
-64 78 80 60 53
-65 46 79 81 54
-66 55 47 80 82
-67 56 48 81 83
-68 57 49 82 84
-69 58 50 83 85
-70 59 51 84 86
-71 60 52 85 87
-72 88 46 53 86
-73 89 47 54 87
-74 55 88 90 48
-75 56 89 49 76
-76 102 62 95 75
-77 103 61 63 96
-78 104 62 64 97
-79 105 63 65 98
-80 66 99 91 64
-81 67 100 92 65
-82 66 68 101 93
-83 67 69 102 94
-84 68 70 103 95
-85 69 71 104 96
-86 70 72 105 97
-87 91 71 73 98
-88 99 92 72 74
-89 100 93 73 75
-90 101 61 94 74
-91 80 107 87 120
-92 88 81 106 108
-93 89 82 107 109
-94 110 90 83 108
-95 111 84 76 109
-96 77 110 112 85
-97 78 111 113 86
-98 79 112 114 87
-99 88 80 113 115
-100 89 81 114 116
-101 90 82 115 117
-102 83 116 118 76
-103 77 84 117 119
-104 78 85 118 120
-105 79 106 86 119
-106 132 92 125 105
-107 133 91 93 126
-108 134 92 94 127
-109 135 93 95 128
-110 121 94 96 129
-111 122 95 97 130
-112 123 96 98 131
-113 99 132 124 97
-114 100 133 125 98
-115 99 101 134 126
-116 100 102 135 127
-117 121 101 103 128
-118 122 102 104 129
-119 123 103 105 130
-120 91 124 104 131
-121 110 137 117 150
-122 111 136 138 118
-123 112 137 139 119
-124 113 138 140 120
-125 114 106 139 141
-126 115 107 140 142
-127 143 116 108 141
-128 144 117 109 142
-129 110 143 145 118
-130 111 144 146 119
-131 112 145 147 120
-132 113 146 148 106
-133 114 147 149 107
-134 115 148 150 108
-135 136 116 149 109
-136 122 155 135 162
-137 121 123 156 163
-138 122 124 157 164
-139 165 123 125 158
-140 124 126 159 151
-141 125 127 160 152
-142 126 128 161 153
-143 154 127 129 162
-144 155 128 130 163
-145 156 129 131 164
-146 132 165 157 130
-147 133 158 151 131
-148 132 134 159 152
-149 133 135 160 153
-150 121 154 134 161
-151 167 147 180 140
-152 166 168 148 141
-153 167 169 149 142
-154 143 168 170 150
-155 144 136 169 171
-156 145 137 170 172
-157 146 138 171 173
-158 147 139 172 174
-159 148 140 173 175
-160 176 149 141 174
-161 177 150 142 175
-162 143 176 178 136
-163 144 177 179 137
-164 145 178 180 138
-165 166 146 179 139
-166 165 192 152 185
-167 193 151 153 186
-168 154 187 194 152
-169 155 188 195 153
-170 154 156 189 181
-171 155 157 190 182
-172 156 158 191 183
-173 157 159 192 184
-174 158 160 193 185
-175 159 161 194 186
-176 187 160 162 195
-177 188 181 161 163
-178 189 182 162 164
-179 165 190 183 163
-180 191 151 184 164
-181 177 210 170 197
-182 198 178 171 196
-183 199 179 172 197
-184 198 200 180 173
-185 166 199 201 174
-186 167 200 202 175
-187 176 168 201 203
-188 177 169 202 204
-189 178 170 203 205
-190 179 171 204 206
-191 180 172 205 207
-192 166 173 206 208
-193 209 167 174 207
-194 210 168 175 208
-195 176 209 169 196
-196 222 182 215 195
-197 223 181 183 216
-198 224 182 184 217
-199 225 183 185 218
-200 211 184 186 219
-201 187 220 212 185
-202 188 221 213 186
-203 187 189 222 214
-204 188 190 223 215
-205 189 191 224 216
-206 190 192 225 217
-207 211 191 193 218
-208 212 192 194 219
-209 220 213 193 195
-210 221 181 214 194
-211 200 227 207 240
-212 201 226 228 208
-213 209 202 227 229
-214 210 203 228 230
-215 231 204 196 229
-216 232 205 197 230
-217 198 231 233 206
-218 199 232 234 207
-219 200 233 235 208
-220 209 201 234 236
-221 210 202 235 237
-222 203 236 238 196
-223 204 237 239 197
-224 198 205 238 240
-225 199 226 206 239
-226 212 245 225 252
-227 253 211 213 246
-228 254 212 214 247
-229 255 213 215 248
-230 214 216 249 241
-231 242 215 217 250
-232 243 216 218 251
-233 244 217 219 252
-234 220 253 245 218
-235 221 254 246 219
-236 220 222 255 247
-237 221 223 248 241
-238 242 222 224 249
-239 243 223 225 250
-240 211 244 224 251
-241 257 237 270 230
-242 231 256 258 238
-243 232 257 259 239
-244 233 258 260 240
-245 234 226 259 261
-246 235 227 260 262
-247 236 228 261 263
-248 264 237 229 262
-249 265 238 230 263
-250 231 264 266 239
-251 232 265 267 240
-252 233 266 268 226
-253 234 267 269 227
-254 235 268 270 228
-255 256 236 269 229
-256 242 12 255 5
-257 243 13 6 241
-258 242 244 14 7
-259 243 245 15 8
-260 1 244 246 9
-261 2 245 247 10
-262 11 3 246 248
-263 12 4 247 249
-264 13 5 248 250
-265 14 6 249 251
-266 15 7 250 252
-267 253 1 8 251
-268 254 2 9 252
-269 253 255 3 10
-270 11 254 4 241
0