M_{22}.2

{L_{2}(11) ≤ \atop L_{2}(11).2} 1344 {1a^{±} + 21a^{±} + 55a^{±} + 154a^{±} + 210a^{±} + \atop 231a^{±}} 12

Character Numbers: [ 1, 2, 3, 4, 9, 10, 13, 14, 15, 16, 17, 18 ]

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 55 55 55 55 66 66 165 165 330 330
χ_{2} 1 −1 −55 −55 55 55 −66 66 −165 165 −330 330
χ_{3} 1 −1 25 −15 −25 15 6 −6 −45 45 30 −30
χ_{4} 1 1 −25 15 −25 15 −6 −6  45 45 −30 −30
χ_{5} 1 1 13 13 13 13 −18 −18 −3 −3 −6 −6
χ_{6} 1 −1 −13 −13 13 13 18 −18  3 −3  6 −6
χ_{7} 1 1  7 −5  7 −5  6  6  9  9 −18 −18
χ_{8} 1 −1 −7  5  7 −5 −6  6 −9  9  18 −18
χ_{9} 1 −1  3  7 −3 −7  6 −6 −1  1 −14 14
χ_{10} 1 1 −3 −7 −3 −7 −6 −6  1  1  14 14
χ_{11} 1 −1  3 −5 −3 5 −6  6  11 −11 −2  2
χ_{12} 1 1 −3  5 −3 5  6  6 −11 −11  2  2

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