Graph forms
for C4 [ 168, 27 ] = Pr_56(1,33,37,13)
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On this page are computer-accessible forms for the graph C4[ 168, 27 ] =
Pr_56(1,33,37,13).
(I) Following is a form readable by MAGMA:
g:=Graph<168|{ {2, 3}, {52, 53}, {50, 51}, {48, 49}, {46, 47}, {44, 45}, {42,
43}, {40, 41}, {38, 39}, {36, 37}, {34, 35}, {32, 33}, {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}, {54, 55}, {1, 2}, {53, 54}, {49, 50}, {45, 46},
{41, 42}, {37, 38}, {33, 34}, {5, 6}, {9, 10}, {13, 14}, {17, 18}, {21, 22},
{25, 26}, {29, 30}, {3, 4}, {51, 52}, {43, 44}, {35, 36}, {11, 12}, {19, 20},
{27, 28}, {114, 127}, {146, 159}, {144, 157}, {130, 143}, {128, 141}, {7, 8},
{145, 158}, {129, 142}, {39, 40}, {23, 24}, {55, 56}, {113, 126}, {131, 144},
{143, 156}, {139, 152}, {135, 148}, {132, 145}, {142, 155}, {140, 153}, {134,
147}, {40, 63}, {141, 154}, {133, 146}, {35, 58}, {39, 62}, {37, 60}, {34, 57},
{38, 61}, {136, 149}, {138, 151}, {15, 16}, {137, 150}, {47, 48}, {36, 59}, {80,
117}, {82, 119}, {88, 125}, {90, 127}, {81, 118}, {89, 126}, {83, 120}, {87,
124}, {84, 121}, {86, 123}, {85, 122}, {147, 160}, {155, 168}, {151, 164}, {148,
161}, {150, 163}, {149, 162}, {1, 57}, {2, 58}, {3, 59}, {4, 60}, {5, 61}, {6,
62}, {7, 63}, {64, 120}, {65, 121}, {66, 122}, {67, 123}, {68, 124}, {69, 125},
{70, 126}, {71, 127}, {1, 56}, {79, 116}, {76, 113}, {154, 167}, {152, 165},
{78, 115}, {31, 32}, {153, 166}, {77, 114}, {8, 64}, {47, 103}, {46, 102}, {45,
101}, {44, 100}, {43, 99}, {42, 98}, {41, 97}, {40, 96}, {9, 65}, {10, 66}, {11,
67}, {12, 68}, {13, 69}, {14, 70}, {15, 71}, {24, 80}, {25, 81}, {26, 82}, {27,
83}, {28, 84}, {29, 85}, {30, 86}, {31, 87}, {56, 112}, {57, 113}, {58, 114},
{59, 115}, {60, 116}, {61, 117}, {62, 118}, {63, 119}, {16, 95}, {32, 111}, {1,
80}, {33, 112}, {3, 82}, {5, 84}, {7, 86}, {9, 88}, {11, 90}, {13, 92}, {15,
94}, {2, 81}, {6, 85}, {10, 89}, {14, 93}, {4, 83}, {12, 91}, {16, 72}, {52,
108}, {51, 107}, {50, 106}, {49, 105}, {48, 104}, {17, 73}, {18, 74}, {19, 75},
{20, 76}, {21, 77}, {22, 78}, {23, 79}, {53, 109}, {54, 110}, {55, 111}, {8,
87}, {41, 64}, {47, 70}, {45, 68}, {43, 66}, {42, 65}, {46, 69}, {44, 67}, {17,
96}, {31, 110}, {19, 98}, {21, 100}, {23, 102}, {25, 104}, {27, 106}, {29, 108},
{18, 97}, {22, 101}, {26, 105}, {30, 109}, {20, 99}, {48, 71}, {28, 107}, {56,
79}, {32, 88}, {39, 95}, {38, 94}, {37, 93}, {36, 92}, {35, 91}, {34, 90}, {33,
89}, {49, 72}, {51, 74}, {53, 76}, {55, 78}, {50, 73}, {54, 77}, {24, 103}, {52,
75}, {59, 152}, {63, 156}, {60, 153}, {62, 155}, {61, 154}, {58, 151}, {57,
150}, {72, 128}, {73, 129}, {74, 130}, {75, 131}, {76, 132}, {77, 133}, {78,
134}, {79, 135}, {88, 144}, {89, 145}, {90, 146}, {91, 147}, {92, 148}, {93,
149}, {94, 150}, {95, 151}, {104, 160}, {105, 161}, {106, 162}, {107, 163},
{108, 164}, {109, 165}, {110, 166}, {111, 167}, {117, 160}, {125, 168}, {119,
162}, {118, 161}, {80, 136}, {81, 137}, {82, 138}, {83, 139}, {84, 140}, {85,
141}, {86, 142}, {87, 143}, {112, 168}, {91, 128}, {124, 167}, {120, 163}, {95,
132}, {64, 157}, {123, 166}, {121, 164}, {66, 159}, {92, 129}, {94, 131}, {65,
158}, {122, 165}, {93, 130}, {67, 160}, {71, 164}, {75, 168}, {68, 161}, {70,
163}, {96, 133}, {98, 135}, {104, 141}, {106, 143}, {112, 149}, {69, 162}, {97,
134}, {105, 142}, {99, 136}, {103, 140}, {116, 159}, {72, 165}, {74, 167}, {100,
137}, {102, 139}, {113, 156}, {115, 158}, {73, 166}, {101, 138}, {114, 157},
{115, 128}, {127, 140}, {123, 136}, {119, 132}, {116, 129}, {126, 139}, {124,
137}, {118, 131}, {117, 130}, {125, 138}, {96, 152}, {97, 153}, {98, 154}, {99,
155}, {100, 156}, {101, 157}, {102, 158}, {103, 159}, {107, 144}, {111, 148},
{108, 145}, {122, 135}, {120, 133}, {110, 147}, {109, 146}, {121, 134} }>;
(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, 57)(3, 113)(4, 76)(5, 53)(6, 109)(7, 165)(8, 72)(9, 49)(10, 105)(11,
161)(12, 68)(13, 45)(14, 101)(15, 157)(16, 64)(17, 41)(18, 97)(19, 153)(20,
60)(21, 37)(22, 93)(23, 149)(24, 112)(25, 33)(26, 89)(27, 145)(28, 108)(30,
85)(31, 141)(32, 104)(34, 81)(35, 137)(36, 100)(38, 77)(39, 133)(40, 96)(42,
73)(43, 129)(44, 92)(46, 69)(47, 125)(48, 88)(50, 65)(51, 121)(52, 84)(54,
61)(55, 117)(56, 80)(58, 150)(59, 156)(62, 146)(63, 152)(66, 142)(67, 148)(70,
138)(71, 144)(74, 134)(75, 140)(78, 130)(79, 136)(82, 126)(83, 132)(86, 122)(87,
128)(90, 118)(91, 124)(94, 114)(95, 120)(98, 166)(99, 116)(102, 162)(103,
168)(106, 158)(107, 164)(110, 154)(111, 160)(115, 143)(119, 139)(123, 135)(127,
131)(147, 167)(151, 163)(155, 159) (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, 56)(3, 55)(4, 54)(5, 53)(6, 52)(7, 51)(8, 50)(9, 49)(10, 48)(11, 47)(12,
46)(13, 45)(14, 44)(15, 43)(16, 42)(17, 41)(18, 40)(19, 39)(20, 38)(21, 37)(22,
36)(23, 35)(24, 34)(25, 33)(26, 32)(27, 31)(28, 30)(57, 80)(58, 79)(59, 78)(60,
77)(61, 76)(62, 75)(63, 74)(64, 73)(65, 72)(66, 71)(67, 70)(68, 69)(81, 112)(82,
111)(83, 110)(84, 109)(85, 108)(86, 107)(87, 106)(88, 105)(89, 104)(90, 103)(91,
102)(92, 101)(93, 100)(94, 99)(95, 98)(96, 97)(113, 117)(114, 116)(118,
168)(119, 167)(120, 166)(121, 165)(122, 164)(123, 163)(124, 162)(125, 161)(126,
160)(127, 159)(128, 158)(129, 157)(130, 156)(131, 155)(132, 154)(133, 153)(134,
152)(135, 151)(136, 150)(137, 149)(138, 148)(139, 147)(140, 146)(141, 145)(142,
144)
c: (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)
C4[ 168, 27 ]
168
-1 56 2 57 80
-2 1 3 58 81
-3 2 4 59 82
-4 3 5 60 83
-5 4 6 61 84
-6 5 7 62 85
-7 6 8 63 86
-8 7 9 64 87
-9 88 8 10 65
-10 11 66 89 9
-11 12 67 90 10
-12 11 13 68 91
-13 12 14 69 92
-14 13 15 70 93
-15 14 16 71 94
-16 15 17 72 95
-17 16 18 73 96
-18 17 19 74 97
-19 18 20 75 98
-20 99 19 21 76
-21 22 77 100 20
-22 23 78 101 21
-23 22 24 79 102
-24 23 25 80 103
-25 24 26 81 104
-26 25 27 82 105
-27 26 28 83 106
-28 27 29 84 107
-29 28 30 85 108
-30 29 31 86 109
-31 110 30 32 87
-32 33 88 111 31
-33 34 89 112 32
-34 33 35 57 90
-35 34 36 58 91
-36 35 37 59 92
-37 36 38 60 93
-38 37 39 61 94
-39 38 40 62 95
-40 39 41 63 96
-41 40 42 64 97
-42 41 43 65 98
-43 44 66 99 42
-44 45 67 100 43
-45 44 46 68 101
-46 45 47 69 102
-47 46 48 70 103
-48 47 49 71 104
-49 48 50 72 105
-50 49 51 73 106
-51 50 52 74 107
-52 51 53 75 108
-53 52 54 76 109
-54 55 77 110 53
-55 56 78 111 54
-56 55 1 79 112
-57 1 34 113 150
-58 2 35 114 151
-59 3 36 115 152
-60 4 37 116 153
-61 154 5 38 117
-62 155 6 39 118
-63 156 7 40 119
-64 157 8 41 120
-65 121 158 9 42
-66 122 159 10 43
-67 11 44 123 160
-68 12 45 124 161
-69 13 46 125 162
-70 14 47 126 163
-71 15 48 127 164
-72 165 16 49 128
-73 166 17 50 129
-74 167 18 51 130
-75 168 19 52 131
-76 132 113 20 53
-77 133 114 21 54
-78 22 55 134 115
-79 23 56 135 116
-80 1 24 136 117
-81 2 25 137 118
-82 3 26 138 119
-83 4 27 139 120
-84 121 5 28 140
-85 122 6 29 141
-86 123 7 30 142
-87 143 124 8 31
-88 144 125 9 32
-89 33 145 126 10
-90 11 34 146 127
-91 12 35 147 128
-92 13 36 148 129
-93 14 37 149 130
-94 15 38 150 131
-95 132 16 39 151
-96 133 17 40 152
-97 134 18 41 153
-98 154 135 19 42
-99 155 136 20 43
-100 44 156 137 21
-101 22 45 157 138
-102 23 46 158 139
-103 24 47 159 140
-104 25 48 160 141
-105 26 49 161 142
-106 143 27 50 162
-107 144 28 51 163
-108 145 29 52 164
-109 165 146 30 53
-110 166 147 31 54
-111 55 167 148 32
-112 33 56 168 149
-113 57 156 126 76
-114 77 58 157 127
-115 78 59 158 128
-116 79 60 159 129
-117 80 61 160 130
-118 81 62 161 131
-119 132 82 63 162
-120 133 83 64 163
-121 134 84 65 164
-122 66 165 135 85
-123 67 166 136 86
-124 68 167 137 87
-125 88 69 168 138
-126 89 113 70 139
-127 90 114 71 140
-128 91 115 72 141
-129 92 116 73 142
-130 143 93 117 74
-131 144 94 118 75
-132 145 95 119 76
-133 77 146 96 120
-134 121 78 147 97
-135 122 79 148 98
-136 99 123 80 149
-137 100 124 81 150
-138 101 125 82 151
-139 102 126 83 152
-140 103 127 84 153
-141 154 104 128 85
-142 155 105 129 86
-143 156 106 130 87
-144 88 157 107 131
-145 132 89 158 108
-146 133 90 159 109
-147 110 134 91 160
-148 111 135 92 161
-149 112 136 93 162
-150 57 137 94 163
-151 58 138 95 164
-152 165 59 139 96
-153 166 60 140 97
-154 167 61 141 98
-155 99 168 62 142
-156 143 100 113 63
-157 144 101 114 64
-158 145 102 115 65
-159 66 146 103 116
-160 67 147 104 117
-161 68 148 105 118
-162 69 149 106 119
-163 70 150 107 120
-164 121 71 151 108
-165 122 72 152 109
-166 110 123 73 153
-167 154 111 124 74
-168 155 112 125 75
0