M_{12}.2

3^{2} : 2.A_{4} ≤ 3^{2}.2.S_{4}

880 1a^{±} + 11ab + 45a^{±} + 54a^{±} + 55a^{±}bc + 99a^{±} +
120a^{±}

14

Character Numbers: [ 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17 ]

S_{1} S_{2}  S_{3} S_{4} S_{5} S_{6}  S_{7}  S_{8} S_{9} S_{10} S_{11} S_{12}  S_{13} S_{14}
χ_{1} 1 1  8 24 27 27  36  36 72 72  72  72  216 216
χ_{2} 1 1 −8 24 27 27 −36 −36 72 72 −72 −72 −216 216
χ_{3} 1 1  0 −8 15 15  0  0 −24 −24  0  0  0 24
χ_{4} 1 −1  0 0 3 −3  12 −12 16 −16  8 −8  0  0
χ_{5} 1 −1  0 0 3 −3 −12  12 16 −16 −8  8  0  0
χ_{6} 1 1 2r5 2 5 5 −2r5 −2r5  6  6 −4r5 −4r5 10r5 −26
χ_{7} 1 1 −2r5 2 5 5 2r5 2r5  6  6 4r5 4r5 −10r5 −26
χ_{8} 1 1  6 10 −3 −3  6  6 −6 −6  0  0 −18  6
χ_{9} 1 1 −6 10 −3 −3 −6 −6 −6 −6  0  0  18  6
χ_{10} 1 −1  0 0 −9 9  0  0  0  0  0  0  0  0
χ_{11} 1 1  2 −6 −3 −3 −6 −6  2  2  8  8  −6  6
χ_{12} 1 1 −2 −6 −3 −3  6  6  2  2 −8 −8  6  6
χ_{13} 1 −1  0 0 3 −3 2r3 −2r3 −6  6 −6r3 6r3  0  0
χ_{14} 1 −1  0 0 3 −3 −2r3 2r3 −6  6 6r3 −6r3  0  0

Ramanujan Graphs: [ 2, 3, 4, 5, 6, 7, 8 ], [ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ], [ 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ], [ 2, 3, 4, 5, 6, 7, 8, 9, 11 ], [ 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 14 ], [ 2, 3, 4, 5, 6, 7, 8, 9, 12 ], [ 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14 ], [ 2, 3, 4, 5, 6, 7, 8, 10, 11 ], [ 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14 ], [ 2, 3, 4, 5, 6, 7, 8, 10, 12 ], [ 2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14 ], [ 2, 3, 4, 5, 6, 7, 8, 13, 14 ], [ 2, 3, 4, 5, 6, 7, 9, 10, 11, 12 ] , [ 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14 ], [ 2, 3, 4, 5, 6, 7, 9, 10, 13 ], [ 2, 3, 4, 5, 6, 7, 9, 11, 12, 13, 14 ], [ 2, 3, 4, 5, 6, 7, 9, 11, 13, 14 ], [ 2, 3, 4, 5, 6, 7, 9, 12, 13, 14 ], [ 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14 ], [ 2, 3, 4, 5, 6, 7, 10, 11, 13, 14 ], [ 2, 3, 4, 5, 6, 7, 10, 12, 13, 14 ], [ 2, 3, 4, 5, 6, 7, 11, 13, 14 ], [ 2, 3, 4, 5, 6, 7, 12, 13, 14 ], [ 2, 3, 4, 5, 6, 7, 13, 14 ], [ 2, 3, 4, 5, 6, 8, 9, 10, 11, 12 ], [ 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14 ], [ 2, 3, 4, 5, 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