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On this page are computer-accessible forms for the graph C4[ 42, 3 ] = PS(6,7;2).

(I) Following is a form readable by MAGMA:

g:=Graph<42|{ {28, 29}, {13, 15}, {20, 23}, {18, 22}, {19, 23}, {10, 15}, {34, 39}, {32, 37}, {19, 22}, {24, 30}, {35, 37}, {34, 36}, {25, 31}, {33, 38}, {1, 9}, {23, 31}, {6, 14}, {5, 13}, {4, 12}, {3, 11}, {2, 10}, {22, 30}, {32, 41}, {2, 8}, {7, 13}, {6, 12}, {3, 9}, {16, 26}, {17, 27}, {23, 29}, {16, 27}, {35, 40}, {33, 42}, {20, 24}, {21, 25}, {17, 28}, {21, 24}, {4, 10}, {5, 11}, {18, 28}, {1, 14}, {7, 8}, {15, 26}, {15, 25}, {8, 17}, {10, 19}, {12, 21}, {9, 18}, {11, 16}, {8, 20}, {9, 21}, {12, 17}, {14, 19}, {14, 16}, {11, 20}, {13, 18}, {4, 36}, {7, 39}, {6, 38}, {5, 37}, {5, 36}, {7, 38}, {6, 37}, {1, 39}, {1, 40}, {3, 42}, {2, 40}, {3, 41}, {2, 41}, {4, 42}, {29, 41}, {30, 42}, {22, 35}, {31, 40}, {24, 32}, {27, 35}, {26, 34}, {25, 33}, {30, 39}, {26, 32}, {27, 33}, {29, 38}, {31, 36}, {28, 34} }>;

(II) A more general form is to represent the graph as the orbit of {28, 29} under the group generated by the following permutations:

a: (1, 8, 5, 22, 29, 26)(2, 11, 35, 23, 32, 14)(3, 27, 31, 24, 6, 10)(4, 42, 33, 25, 21, 12)(7, 13, 18, 28, 34, 39)(9, 17, 36, 30, 38, 15)(16, 40, 20, 37, 19, 41)
b: (3, 7)(4, 15)(5, 33)(6, 16)(8, 41)(9, 39)(11, 38)(12, 26)(13, 42)(17, 32)(18, 30)(20, 29)(21, 34)(24, 28)(25, 36)(27, 37)
c: (2, 7)(3, 6)(4, 5)(9, 14)(10, 13)(11, 12)(16, 21)(17, 20)(18, 19)(23, 28)(24, 27)(25, 26)(30, 35)(31, 34)(32, 33)(37, 42)(38, 41)(39, 40)
d: (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)

(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[ 42, 3 ]
42
-1 14 39 40 9
-2 40 8 41 10
-3 11 41 9 42
-4 12 36 42 10
-5 11 13 36 37
-6 12 14 37 38
-7 13 38 39 8
-8 2 17 7 20
-9 1 3 18 21
-10 2 4 15 19
-11 3 5 16 20
-12 4 6 17 21
-13 15 5 7 18
-14 1 16 6 19
-15 13 25 26 10
-16 11 14 26 27
-17 12 27 28 8
-18 22 13 28 9
-19 22 23 14 10
-20 11 23 24 8
-21 12 24 25 9
-22 35 18 19 30
-23 29 19 20 31
-24 30 20 21 32
-25 33 15 31 21
-26 34 15 16 32
-27 33 35 16 17
-28 34 17 18 29
-29 23 38 28 41
-30 22 24 39 42
-31 23 25 36 40
-32 24 26 37 41
-33 25 27 38 42
-34 36 26 28 39
-35 22 37 27 40
-36 34 4 5 31
-37 35 5 6 32
-38 33 6 7 29
-39 1 34 7 30
-40 1 2 35 31
-41 2 3 29 32
-42 33 3 4 30
0

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