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On this page are computer-accessible forms for the graph C4[ 156, 10 ] = PS(4,39;5).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {74, 79} under the group generated by the following permutations:

a: (2, 39)(3, 38)(4, 37)(5, 36)(6, 35)(7, 34)(8, 33)(9, 32)(10, 31)(11, 30)(12, 29)(13, 28)(14, 27)(15, 26)(16, 25)(17, 24)(18, 23)(19, 22)(20, 21)(41, 78)(42, 77)(43, 76)(44, 75)(45, 74)(46, 73)(47, 72)(48, 71)(49, 70)(50, 69)(51, 68)(52, 67)(53, 66)(54, 65)(55, 64)(56, 63)(57, 62)(58, 61)(59, 60)(80, 117)(81, 116)(82, 115)(83, 114)(84, 113)(85, 112)(86, 111)(87, 110)(88, 109)(89, 108)(90, 107)(91, 106)(92, 105)(93, 104)(94, 103)(95, 102)(96, 101)(97, 100)(98, 99)(119, 156)(120, 155)(121, 154)(122, 153)(123, 152)(124, 151)(125, 150)(126, 149)(127, 148)(128, 147)(129, 146)(130, 145)(131, 144)(132, 143)(133, 142)(134, 141)(135, 140)(136, 139)(137, 138)
b: (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)
c: (1, 40, 79, 118)(2, 45, 104, 126)(3, 50, 90, 134)(4, 55, 115, 142)(5, 60, 101, 150)(6, 65, 87, 119)(7, 70, 112, 127)(8, 75, 98, 135)(9, 41, 84, 143)(10, 46, 109, 151)(11, 51, 95, 120)(12, 56, 81, 128)(13, 61, 106, 136)(14, 66, 92, 144)(15, 71, 117, 152)(16, 76, 103, 121)(17, 42, 89, 129)(18, 47, 114, 137)(19, 52, 100, 145)(20, 57, 86, 153)(21, 62, 111, 122)(22, 67, 97, 130)(23, 72, 83, 138)(24, 77, 108, 146)(25, 43, 94, 154)(26, 48, 80, 123)(27, 53, 105, 131)(28, 58, 91, 139)(29, 63, 116, 147)(30, 68, 102, 155)(31, 73, 88, 124)(32, 78, 113, 132)(33, 44, 99, 140)(34, 49, 85, 148)(35, 54, 110, 156)(36, 59, 96, 125)(37, 64, 82, 133)(38, 69, 107, 141)(39, 74, 93, 149)

(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.

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&Graph
C4[ 156, 10 ]
156
-1 78 126 149 41
-2 127 40 150 42
-3 128 41 151 43
-4 44 129 42 152
-5 45 130 43 153
-6 44 154 46 131
-7 132 45 155 47
-8 133 46 156 48
-9 134 47 49 118
-10 135 48 50 119
-11 136 49 51 120
-12 121 137 50 52
-13 122 138 51 53
-14 123 139 52 54
-15 55 124 140 53
-16 56 125 141 54
-17 55 57 126 142
-18 143 56 58 127
-19 144 57 59 128
-20 145 58 60 129
-21 146 59 61 130
-22 147 60 62 131
-23 132 148 61 63
-24 133 149 62 64
-25 134 150 63 65
-26 66 135 151 64
-27 67 136 152 65
-28 66 68 137 153
-29 154 67 69 138
-30 155 68 70 139
-31 156 69 71 140
-32 70 72 118 141
-33 71 73 119 142
-34 143 72 74 120
-35 121 144 73 75
-36 122 145 74 76
-37 77 123 146 75
-38 78 124 147 76
-39 77 125 148 40
-40 2 113 39 84
-41 1 3 114 85
-42 2 4 115 86
-43 3 5 116 87
-44 88 4 6 117
-45 89 79 5 7
-46 90 80 6 8
-47 91 81 7 9
-48 92 82 8 10
-49 11 93 83 9
-50 12 94 84 10
-51 11 13 95 85
-52 12 14 96 86
-53 13 15 97 87
-54 88 14 16 98
-55 99 89 15 17
-56 100 90 16 18
-57 101 91 17 19
-58 102 92 18 20
-59 103 93 19 21
-60 22 104 94 20
-61 23 105 95 21
-62 22 24 106 96
-63 23 25 107 97
-64 24 26 108 98
-65 99 25 27 109
-66 110 100 26 28
-67 111 101 27 29
-68 112 102 28 30
-69 113 103 29 31
-70 114 104 30 32
-71 33 115 105 31
-72 34 116 106 32
-73 33 35 117 107
-74 34 79 36 108
-75 35 80 37 109
-76 110 36 81 38
-77 111 37 82 39
-78 1 112 38 83
-79 132 143 45 74
-80 133 144 46 75
-81 134 145 47 76
-82 77 135 146 48
-83 78 136 147 49
-84 137 148 50 40
-85 138 149 51 41
-86 139 150 52 42
-87 140 151 53 43
-88 44 141 152 54
-89 55 45 142 153
-90 143 154 56 46
-91 144 155 57 47
-92 145 156 58 48
-93 146 59 49 118
-94 147 60 50 119
-95 148 61 51 120
-96 121 149 62 52
-97 122 150 63 53
-98 123 151 64 54
-99 55 124 152 65
-100 66 56 125 153
-101 154 67 57 126
-102 155 68 58 127
-103 156 69 59 128
-104 70 60 118 129
-105 71 61 119 130
-106 72 62 120 131
-107 121 132 73 63
-108 122 133 74 64
-109 123 134 75 65
-110 66 124 135 76
-111 77 67 125 136
-112 78 68 126 137
-113 69 127 138 40
-114 70 128 139 41
-115 71 129 140 42
-116 72 130 141 43
-117 44 73 131 142
-118 93 104 9 32
-119 33 94 105 10
-120 11 34 95 106
-121 12 35 96 107
-122 13 36 97 108
-123 14 37 98 109
-124 99 110 15 38
-125 100 111 16 39
-126 1 101 112 17
-127 2 102 113 18
-128 3 103 114 19
-129 4 104 115 20
-130 5 105 116 21
-131 22 6 106 117
-132 23 79 7 107
-133 24 80 8 108
-134 25 81 9 109
-135 110 26 82 10
-136 11 111 27 83
-137 12 112 28 84
-138 13 113 29 85
-139 14 114 30 86
-140 15 115 31 87
-141 88 16 116 32
-142 33 89 17 117
-143 34 79 90 18
-144 35 80 91 19
-145 36 81 92 20
-146 37 82 93 21
-147 22 38 83 94
-148 23 39 84 95
-149 1 24 85 96
-150 2 25 86 97
-151 3 26 87 98
-152 88 99 4 27
-153 89 100 5 28
-154 90 101 6 29
-155 91 102 7 30
-156 92 103 8 31
0

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