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