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On this page are computer-accessible forms for the graph C4[ 27, 2 ] = PS(3,9;2).

(I) Following is a form readable by MAGMA:

g:=Graph<27|{ {17, 19}, {9, 10}, {18, 20}, {16, 23}, {2, 10}, {7, 15}, {6, 14}, {5, 13}, {4, 12}, {3, 11}, {17, 24}, {1, 11}, {5, 15}, {4, 14}, {16, 27}, {18, 25}, {2, 12}, {3, 13}, {10, 26}, {11, 27}, {6, 20}, {7, 21}, {1, 18}, {7, 20}, {6, 19}, {15, 26}, {13, 24}, {1, 23}, {6, 16}, {5, 19}, {7, 17}, {14, 25}, {8, 16}, {9, 17}, {1, 24}, {15, 22}, {13, 20}, {3, 26}, {2, 24}, {3, 25}, {8, 18}, {2, 25}, {14, 21}, {12, 23}, {8, 21}, {11, 22}, {4, 26}, {5, 27}, {8, 22}, {9, 23}, {4, 27}, {9, 22}, {10, 21}, {12, 19} }>;

(II) A more general form is to represent the graph as the orbit of {17, 19} under the group generated by the following permutations:

a: (1, 10, 19)(2, 17, 23)(3, 15, 27)(4, 13, 22)(5, 11, 26)(6, 18, 21)(7, 16, 25)(8, 14, 20)(9, 12, 24)
b: (2, 9)(3, 8)(4, 7)(5, 6)(11, 18)(12, 17)(13, 16)(14, 15)(20, 27)(21, 26)(22, 25)(23, 24)
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)

(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[ 27, 2 ]
27
-1 11 23 24 18
-2 12 24 25 10
-3 11 13 25 26
-4 12 14 26 27
-5 13 15 27 19
-6 14 16 19 20
-7 15 17 20 21
-8 22 16 18 21
-9 22 23 17 10
-10 2 26 9 21
-11 22 1 3 27
-12 23 2 4 19
-13 24 3 5 20
-14 25 4 6 21
-15 22 26 5 7
-16 23 27 6 8
-17 24 7 19 9
-18 1 25 8 20
-19 12 5 6 17
-20 13 6 7 18
-21 14 7 8 10
-22 11 15 8 9
-23 1 12 16 9
-24 1 2 13 17
-25 2 3 14 18
-26 3 4 15 10
-27 11 4 5 16
0

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