Graph forms
for C4 [ 216, 26 ] =
PL(WH_36(9,1,19,24),[4^27,9^12])
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On this page are computer-accessible forms for the graph C4[ 216, 26 ] =
PL(WH_36(9,1,19,24),[4^27,9^12]).
(I) Following is a form readable by MAGMA:
g:=Graph<216|{ {106, 109}, {100, 109}, {97, 109}, {101, 113}, {106, 112}, {107,
112}, {83, 114}, {77, 111}, {79, 109}, {75, 111}, {87, 114}, {85, 114}, {81,
121}, {90, 113}, {67, 113}, {68, 119}, {67, 118}, {78, 123}, {68, 114}, {88,
110}, {86, 110}, {77, 116}, {66, 120}, {84, 110}, {76, 115}, {49, 112}, {50,
115}, {45, 111}, {48, 116}, {61, 123}, {48, 121}, {54, 124}, {55, 125}, {34,
115}, {43, 120}, {46, 125}, {45, 126}, {60, 111}, {32, 118}, {34, 120}, {37,
121}, {50, 110}, {47, 115}, {40, 116}, {41, 118}, {29, 125}, {26, 120}, {28,
126}, {19, 112}, {24, 123}, {17, 116}, {25, 124}, {31, 121}, {26, 125}, {21,
124}, {19, 127}, {23, 122}, {16, 126}, {24, 118}, {10, 122}, {4, 117}, {6, 117},
{12, 127}, {1, 117}, {8, 124}, {2, 117}, {9, 126}, {6, 113}, {15, 119}, {3,
122}, {1, 123}, {5, 127}, {3, 127}, {11, 119}, {7, 122}, {8, 119}, {19, 147},
{65, 193}, {69, 197}, {32, 161}, {41, 168}, {70, 199}, {80, 209}, {38, 164},
{59, 185}, {78, 204}, {60, 191}, {75, 200}, {9, 141}, {71, 195}, {73, 205}, {20,
145}, {40, 173}, {23, 146}, {65, 196}, {14, 136}, {35, 165}, {33, 166}, {55,
176}, {51, 180}, {28, 148}, {92, 212}, {43, 163}, {29, 149}, {67, 203}, {71,
207}, {73, 192}, {79, 198}, {18, 152}, {53, 191}, {72, 194}, {22, 157}, {63,
180}, {15, 131}, {61, 177}, {13, 128}, {93, 208}, {31, 146}, {19, 157}, {56,
182}, {44, 162}, {69, 203}, {7, 136}, {25, 150}, {58, 181}, {44, 188}, {68,
212}, {22, 135}, {41, 184}, {66, 211}, {40, 186}, {80, 194}, {11, 152}, {48,
163}, {30, 141}, {15, 156}, {64, 211}, {8, 156}, {94, 202}, {47, 187}, {27,
143}, {4, 145}, {59, 174}, {60, 169}, {62, 171}, {70, 211}, {18, 132}, {86,
192}, {85, 195}, {6, 145}, {10, 146}, {89, 193}, {1, 152}, {47, 182}, {76, 213},
{2, 152}, {92, 198}, {54, 172}, {52, 174}, {22, 141}, {57, 162}, {13, 145}, {39,
187}, {42, 183}, {20, 138}, {87, 201}, {55, 169}, {27, 133}, {72, 214}, {12,
147}, {88, 199}, {53, 170}, {74, 213}, {7, 167}, {54, 150}, {39, 135}, {21,
181}, {6, 167}, {3, 161}, {104, 202}, {17, 179}, {56, 155}, {5, 161}, {37, 129},
{4, 161}, {38, 131}, {36, 129}, {22, 179}, {63, 154}, {108, 202}, {30, 185},
{101, 194}, {52, 147}, {29, 181}, {100, 204}, {99, 203}, {30, 182}, {62, 150},
{14, 167}, {44, 133}, {43, 130}, {42, 131}, {33, 136}, {12, 166}, {108, 198},
{96, 202}, {26, 176}, {61, 151}, {16, 187}, {17, 186}, {35, 143}, {49, 157},
{27, 182}, {25, 183}, {50, 156}, {60, 146}, {9, 166}, {24, 183}, {24, 168}, {62,
142}, {21, 164}, {97, 208}, {63, 142}, {3, 177}, {14, 186}, {53, 129}, {63,
139}, {1, 183}, {98, 212}, {45, 155}, {35, 149}, {31, 169}, {16, 166}, {7, 177},
{59, 141}, {36, 147}, {56, 143}, {52, 140}, {58, 130}, {10, 179}, {49, 136},
{45, 148}, {27, 162}, {26, 163}, {20, 173}, {2, 184}, {46, 148}, {39, 157}, {37,
159}, {23, 173}, {9, 179}, {46, 149}, {51, 143}, {8, 181}, {28, 162}, {57, 135},
{56, 134}, {34, 156}, {5, 186}, {15, 207}, {65, 129}, {70, 134}, {107, 170},
{14, 204}, {105, 171}, {103, 165}, {16, 210}, {18, 215}, {92, 153}, {23, 210},
{64, 133}, {69, 128}, {71, 130}, {83, 149}, {95, 153}, {103, 160}, {13, 197},
{82, 154}, {5, 204}, {93, 151}, {72, 131}, {100, 175}, {73, 130}, {20, 216},
{102, 170}, {90, 150}, {74, 134}, {75, 135}, {93, 144}, {98, 175}, {81, 159},
{99, 173}, {10, 197}, {96, 175}, {95, 144}, {81, 158}, {75, 155}, {31, 206},
{84, 133}, {74, 155}, {28, 206}, {91, 137}, {71, 148}, {87, 132}, {2, 214},
{106, 190}, {17, 197}, {4, 209}, {107, 190}, {95, 138}, {92, 137}, {91, 142},
{89, 140}, {29, 200}, {13, 216}, {101, 178}, {105, 190}, {101, 189}, {78, 151},
{102, 191}, {82, 139}, {30, 196}, {104, 178}, {103, 189}, {64, 154}, {18, 201},
{69, 158}, {11, 215}, {100, 184}, {21, 201}, {12, 208}, {70, 154}, {81, 140},
{25, 199}, {94, 128}, {88, 134}, {80, 142}, {11, 212}, {33, 193}, {94, 190},
{54, 214}, {36, 196}, {73, 169}, {46, 207}, {85, 180}, {78, 175}, {76, 174},
{80, 178}, {105, 138}, {51, 215}, {96, 132}, {67, 167}, {72, 172}, {108, 137},
{43, 205}, {66, 164}, {90, 189}, {42, 194}, {108, 132}, {104, 128}, {36, 205},
{99, 138}, {98, 139}, {89, 176}, {85, 188}, {38, 207}, {102, 140}, {32, 203},
{96, 139}, {47, 196}, {64, 172}, {68, 168}, {42, 199}, {95, 178}, {53, 216},
{59, 213}, {103, 137}, {77, 163}, {38, 201}, {91, 180}, {86, 185}, {83, 188},
{82, 189}, {62, 209}, {49, 193}, {105, 153}, {51, 195}, {32, 209}, {97, 144},
{90, 171}, {34, 211}, {33, 208}, {57, 200}, {65, 176}, {50, 192}, {86, 164},
{58, 200}, {77, 191}, {35, 215}, {84, 160}, {39, 210}, {106, 159}, {94, 171},
{74, 188}, {83, 165}, {55, 192}, {93, 170}, {89, 174}, {82, 165}, {57, 206},
{76, 187}, {79, 184}, {84, 172}, {104, 144}, {102, 158}, {88, 160}, {44, 213},
{52, 205}, {58, 195}, {40, 210}, {61, 198}, {98, 153}, {91, 160}, {66, 185},
{107, 151}, {37, 216}, {99, 158}, {48, 206}, {97, 159}, {79, 177}, {41, 214},
{87, 168} }>;
(II) A more general form is to represent the graph as the orbit of {106, 109}
under the group generated by the following permutations:
a: (3, 8, 14, 38)(4, 11, 6, 18)(5, 15, 7, 21)(9, 73, 39, 26)(10, 58, 40, 46)(12,
50, 49, 66)(13, 51, 20, 35)(16, 55, 22, 43)(17, 71, 23, 29)(19, 34, 33, 86)(25,
78, 42, 61)(27, 37)(28, 31, 57, 48)(30, 36, 47, 65)(32, 68, 67, 87)(44, 81)(45,
60, 75, 77)(52, 76, 89, 59)(53, 56)(54, 100, 72, 79)(62, 98, 101, 108)(63, 95,
103, 94)(64, 97, 84, 106)(69, 85, 99, 83)(70, 93, 88, 107)(74, 102)(80, 92, 90,
96)(82, 104, 91, 105)(109, 172)(110, 112, 211, 208)(113, 132, 209, 212)(114,
203)(115, 193, 185, 147)(116, 148, 146, 200)(117, 152)(118, 168)(119, 167, 201,
161)(120, 166, 192, 157)(121, 162)(122, 181, 186, 207)(123, 183)(124, 204, 131,
177)(125, 179, 130, 210)(126, 169, 135, 163)(127, 156, 136, 164)(128, 180, 138,
165)(129, 182)(133, 159)(134, 170)(137, 171, 139, 178)(140, 213)(141, 205, 187,
176)(142, 153, 189, 202)(143, 216)(144, 160, 190, 154)(145, 215)(149, 197, 195,
173)(150, 175, 194, 198)(151, 199)(155, 191)(158, 188)(184, 214) (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, 3, 24, 5)(2, 7, 41, 14)(4, 61, 32, 78)(6, 79, 67, 100)(8, 22)(9, 15)(10,
68, 17, 11)(12, 42)(13, 92, 69, 98)(16, 38)(18, 23, 87, 40)(19, 25)(20, 108, 99,
96)(21, 39)(26, 27, 55, 44)(28, 46)(29, 57)(30, 50, 59, 34)(31, 83, 48, 35)(33,
72)(36, 88, 52, 70)(37, 103, 81, 82)(43, 56, 73, 74)(45, 71)(47, 86, 76, 66)(49,
54)(51, 60, 85, 77)(53, 91, 102, 63)(58, 75)(62, 107)(64, 65, 84, 89)(80,
93)(90, 106)(94, 105)(95, 104)(97, 101)(109, 113)(110, 174, 211, 196)(111,
195)(112, 150)(114, 116, 215, 146)(115, 185)(117, 177, 118, 204)(119, 179)(120,
182, 192, 213)(121, 165)(122, 168, 186, 152)(123, 161)(124, 157)(125, 162)(126,
207)(127, 183)(128, 153)(129, 160, 140, 154)(130, 155)(131, 166)(132, 173)(133,
176)(134, 205)(135, 181)(136, 214)(137, 158, 139, 216)(138, 202)(141, 156)(142,
170)(143, 169, 188, 163)(144, 178)(145, 198, 203, 175)(147, 199)(149, 206)(151,
209)(159, 189)(164, 187)(167, 184)(171, 190)(172, 193)(180, 191)(194, 208)(197,
212)(201, 210)
c: (3, 7)(4, 6)(5, 14)(12, 33)(19, 49)(26, 43)(29, 58)(32, 67)(35, 51)(36,
65)(46, 71)(52, 89)(55, 73)(62, 90)(63, 82)(80, 101)(83, 85)(91, 103)(113,
209)(125, 130)(127, 136)(142, 189)(147, 193)(149, 195)(161, 167)(165, 180)(176,
205)
d: (8, 15)(9, 22)(12, 19)(16, 39)(21, 38)(25, 42)(28, 57)(29, 46)(33, 49)(45,
75)(54, 72)(58, 71)(62, 80)(90, 101)(93, 107)(94, 104)(95, 105)(97, 106)(112,
208)(124, 131)(126, 135)(144, 190)(148, 200)(150, 194)(157, 166)(171, 178)(181,
207)
e: (1, 4, 13, 37, 65, 47, 56, 51, 18, 2, 6, 20, 53, 36, 30, 27, 35, 11)(3, 10,
31, 55, 50, 88, 91, 108, 79, 7, 23, 60, 73, 86, 84, 103, 92, 61)(5, 17, 48, 26,
34, 70, 63, 96, 100, 14, 40, 77, 43, 66, 64, 82, 98, 78)(8, 42, 62, 104, 106,
33, 39, 45, 58, 38, 54, 101, 105, 93, 19, 9, 57, 46)(12, 22, 28, 29, 15, 25, 80,
94, 97, 49, 16, 75, 71, 21, 72, 90, 95, 107)(24, 32, 69, 81, 89, 76, 74, 85, 87,
41, 67, 99, 102, 52, 59, 44, 83, 68)(109, 136, 210, 111, 130, 164, 172, 189,
153, 151, 127, 179, 206, 125, 156, 199, 142, 202)(110, 160, 137, 198, 177, 122,
146, 169, 192)(112, 166, 135, 148, 181, 131, 150, 178, 190, 208, 157, 126, 200,
207, 124, 194, 171, 144)(113, 138, 170, 147, 141, 162, 149, 119, 183, 209, 128,
159, 193, 187, 155, 195, 201, 214)(114, 168, 118, 203, 158, 140, 174, 213,
188)(115, 134, 180, 132, 184, 167, 173, 191, 205, 185, 133, 165, 212, 123, 161,
197, 121, 176)(116, 163, 120, 211, 154, 139, 175, 204, 186)(117, 145, 216, 129,
196, 182, 143, 215, 152)
f: (3, 5)(7, 14)(10, 17)(23, 40)(26, 55)(31, 48)(34, 50)(43, 73)(60, 77)(61,
78)(63, 91)(64, 84)(66, 86)(70, 88)(79, 100)(82, 103)(92, 98)(96, 108)(110,
211)(116, 146)(120, 192)(122, 186)(137, 139)(154, 160)(163, 169)(175, 198)(177,
204)
g: (2, 24)(4, 61)(5, 7)(6, 78)(8, 21, 38, 15)(9, 16, 39, 22)(10, 12, 23, 19)(11,
25, 18, 42)(13, 93, 20, 107)(17, 33, 40, 49)(27, 74)(28, 76, 57, 59)(29, 66, 46,
34)(30, 45, 47, 75)(31, 52)(32, 79)(35, 70)(36, 60)(37, 102)(43, 55)(48, 89)(50,
58, 86, 71)(51, 88)(54, 87, 72, 68)(62, 108, 80, 92)(63, 103)(64, 83)(65,
77)(67, 100)(69, 97, 99, 106)(84, 85)(90, 96, 101, 98)(94, 104, 95, 105)(109,
203)(110, 195)(111, 196)(112, 197, 208, 173)(113, 175)(114, 172)(115, 200, 185,
148)(116, 193)(117, 123)(118, 184)(119, 124, 201, 131)(120, 125)(121, 140)(122,
127)(126, 187, 135, 141)(128, 144, 138, 190)(129, 191)(130, 192)(132, 194, 212,
150)(133, 188)(134, 143)(136, 186)(137, 142)(139, 189)(145, 151)(146, 147)(149,
211)(152, 183)(153, 171, 202, 178)(154, 165)(155, 182)(156, 181, 164, 207)(157,
179, 166, 210)(158, 159)(160, 180)(161, 177)(162, 213)(163, 176)(167, 204)(168,
214)(169, 205)(170, 216)(174, 206)(198, 209)(199, 215)
h: (1, 2, 41, 24)(4, 79, 32, 61)(5, 7)(6, 100, 67, 78)(8, 21, 38, 15)(9, 16, 39,
22)(10, 12, 23, 19)(11, 54, 87, 42)(13, 97, 99, 107)(17, 33, 40, 49)(18, 72, 68,
25)(20, 106, 69, 93)(27, 44, 74, 56)(28, 76, 75, 30)(29, 66, 46, 34)(31, 52, 60,
36)(35, 64, 83, 70)(37, 81, 102, 53)(43, 55)(45, 47, 57, 59)(48, 89, 77, 65)(50,
58, 86, 71)(51, 84, 85, 88)(62, 108, 80, 92)(63, 103)(90, 96, 101, 98)(94, 104,
95, 105)(109, 203, 151, 145)(110, 195)(111, 196, 206, 174)(112, 197, 208,
173)(113, 175)(114, 199, 215, 172)(115, 200, 185, 148)(116, 193)(117, 184, 118,
123)(119, 124, 201, 131)(120, 125)(121, 140, 191, 129)(122, 127)(126, 187, 135,
141)(128, 144, 138, 190)(130, 192)(132, 194, 212, 150)(133, 188, 134, 143)(136,
186)(137, 142)(139, 189)(146, 147)(149, 211)(152, 214, 168, 183)(153, 171, 202,
178)(154, 165)(155, 182, 162, 213)(156, 181, 164, 207)(157, 179, 166, 210)(158,
170, 216, 159)(160, 180)(161, 177)(163, 176)(167, 204)(169, 205)(198, 209)
C4[ 216, 26 ]
216
-1 123 117 183 152
-2 214 117 184 152
-3 122 177 127 161
-4 209 145 117 161
-5 127 204 161 186
-6 145 167 113 117
-7 122 177 167 136
-8 156 124 181 119
-9 166 179 126 141
-10 122 146 179 197
-11 212 215 119 152
-12 166 147 127 208
-13 145 128 216 197
-14 167 136 204 186
-15 156 119 207 131
-16 187 166 210 126
-17 179 116 186 197
-18 132 201 215 152
-19 112 157 147 127
-20 145 138 216 173
-21 124 201 181 164
-22 135 157 179 141
-23 122 210 146 173
-24 123 168 183 118
-25 199 124 150 183
-26 176 125 163 120
-27 143 133 182 162
-28 126 148 162 206
-29 200 125 181 149
-30 182 141 185 196
-31 121 146 169 206
-32 209 203 161 118
-33 166 136 193 208
-34 156 211 115 120
-35 143 165 149 215
-36 147 205 129 196
-37 121 159 216 129
-38 201 207 131 164
-39 187 210 135 157
-40 210 116 173 186
-41 168 214 118 184
-42 199 183 194 131
-43 205 130 163 120
-44 133 188 213 162
-45 111 155 126 148
-46 125 148 149 207
-47 187 115 182 196
-48 121 116 206 163
-49 112 157 136 193
-50 110 156 115 192
-51 143 180 215 195
-52 147 205 140 174
-53 191 170 216 129
-54 124 214 150 172
-55 176 125 169 192
-56 143 155 134 182
-57 200 135 162 206
-58 200 181 195 130
-59 213 141 174 185
-60 111 146 169 191
-61 198 177 123 151
-62 209 171 150 142
-63 154 180 139 142
-64 154 133 211 172
-65 176 193 129 196
-66 211 185 120 164
-67 167 113 203 118
-68 168 212 114 119
-69 158 203 128 197
-70 154 199 134 211
-71 148 195 130 207
-72 214 172 194 131
-73 169 192 205 130
-74 155 188 134 213
-75 111 155 200 135
-76 187 213 115 174
-77 111 191 116 163
-78 123 204 151 175
-79 198 177 184 109
-80 209 178 194 142
-81 121 158 159 140
-82 154 165 189 139
-83 165 188 114 149
-84 110 133 160 172
-85 188 114 180 195
-86 110 192 185 164
-87 132 168 201 114
-88 110 199 134 160
-89 176 193 140 174
-90 189 113 171 150
-91 180 137 160 142
-92 198 212 137 153
-93 144 170 151 208
-94 190 202 171 128
-95 144 178 138 153
-96 132 202 139 175
-97 144 159 109 208
-98 212 139 153 175
-99 158 203 138 173
-100 204 184 109 175
-101 178 189 113 194
-102 158 191 170 140
-103 165 189 137 160
-104 144 178 202 128
-105 190 138 171 153
-106 112 190 159 109
-107 112 190 170 151
-108 132 198 202 137
-109 100 79 106 97
-110 88 50 84 86
-111 77 45 60 75
-112 49 106 19 107
-113 67 90 101 6
-114 68 83 85 87
-115 34 47 50 76
-116 77 48 17 40
-117 1 2 4 6
-118 67 24 41 32
-119 11 68 15 8
-120 66 34 26 43
-121 37 48 81 31
-122 23 3 7 10
-123 1 78 24 61
-124 25 8 21 54
-125 55 46 26 29
-126 45 16 28 9
-127 12 3 5 19
-128 13 69 104 94
-129 36 37 53 65
-130 58 71 73 43
-131 15 38 72 42
-132 18 96 108 87
-133 44 27 84 64
-134 88 56 70 74
-135 22 57 39 75
-136 33 14 49 7
-137 91 92 103 108
-138 99 105 95 20
-139 82 63 96 98
-140 89 102 81 52
-141 22 59 30 9
-142 80 91 62 63
-143 56 35 27 51
-144 93 104 95 97
-145 13 4 6 20
-146 23 60 31 10
-147 12 36 19 52
-148 45 46 71 28
-149 35 46 83 29
-150 90 25 62 54
-151 78 93 61 107
-152 11 1 2 18
-153 92 105 95 98
-154 70 82 63 64
-155 45 56 74 75
-156 34 15 50 8
-157 22 49 39 19
-158 99 69 102 81
-159 37 81 106 97
-160 88 91 103 84
-161 3 4 5 32
-162 44 57 27 28
-163 77 26 48 43
-164 66 38 86 21
-165 35 103 82 83
-166 33 12 16 9
-167 67 14 6 7
-168 24 68 41 87
-169 55 60 73 31
-170 102 93 107 53
-171 90 94 105 62
-172 72 84 64 54
-173 99 23 40 20
-174 89 59 52 76
-175 78 100 96 98
-176 55 89 26 65
-177 79 3 61 7
-178 101 80 104 95
-179 22 17 9 10
-180 91 51 63 85
-181 58 29 8 21
-182 56 47 27 30
-183 1 24 25 42
-184 100 2 79 41
-185 66 59 30 86
-186 14 5 17 40
-187 47 16 39 76
-188 44 83 74 85
-189 90 101 103 82
-190 94 105 106 107
-191 77 102 60 53
-192 55 50 73 86
-193 33 89 49 65
-194 101 80 72 42
-195 58 71 51 85
-196 36 47 30 65
-197 13 69 17 10
-198 79 92 61 108
-199 88 25 70 42
-200 57 58 29 75
-201 38 18 21 87
-202 104 94 96 108
-203 99 67 69 32
-204 78 100 14 5
-205 36 73 52 43
-206 57 48 28 31
-207 46 15 38 71
-208 33 12 93 97
-209 80 4 62 32
-210 23 16 39 40
-211 66 34 70 64
-212 11 68 92 98
-213 44 59 74 76
-214 2 72 41 54
-215 11 35 18 51
-216 13 37 20 53
0