McL.2

2.A_{8} ≤ 2.S_{8} 44550 {1a^{±} + 252a^{±} + 1750a^{±} + 5103a^{±} + 5544a^{±} + \atop 9625a^{±}} 12

Character Numbers: [ 1, 2, 7, 8, 14, 15, 24, 25, 26, 27, 30, 31 ]

S_{1} S_{2}  S_{3} S_{4}  S_{5} S_{6} S_{7}  S_{8}  S_{9} S_{10}  S_{11} S_{12}
χ_{1} 1 1 210 210 2240 2240 5040 5040 6720 6720 8064 8064
χ_{2} 1 −1 −210 210 −2240 2240 5040 −5040 −6720 6720 −8064 8064
χ_{3} 1 1  45 45  260 260  90  90 −540 −540  144 144
χ_{4} 1 −1 −45 45 −260 260  90  −90  540 −540 −144 144
χ_{5} 1 1  39 39  −28 −28  72  72  60  60 −144 −144
χ_{6} 1 −1 −39 39  28 −28  72  −72  −60  60  144 −144
χ_{7} 1 1  −5 −5  60  60 −60  −60  60  60  −56 −56
χ_{8} 1 −1  5 −5  −60  60 −60  60  −60  60  56 −56
χ_{9} 1 1 −15 −15  −10 −10  90  90  −30 −30  −36 −36
χ_{10} 1 −1  15 −15  10 −10  90  −90  30 −30  36 −36
χ_{11} 1 1  3  3  −28 −28 −36  −36  −12 −12  72  72
χ_{12} 1 −1  −3  3  28 −28 −36  36  12 −12  −72  72

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