M_{12}.2

A_{6}.2_{2} ≤ A_{6}.2^{2}  264 1a^{±} + 11ab + 54a^{±} + 66a^{±}  7

Character Numbers: [ 1, 2, 3, 7, 8, 9, 10, 14, 15 ]

S_{1} S_{2} S_{3} S_{4}  S_{5}  S_{6} S_{7}  S_{8} S_{9}
χ_{1} 1  4 12 27  36  72 72 108 108
χ_{2} 1 −4 12 27 −36 −72 72 −108 108
χ_{3} 1 0 −4 15 0 0 −24 0 12
χ_{4} 1 −r5 1 5 2r5 4r5  6 −5r5 −13
χ_{5} 1 r5 1 5 −2r5 −4r5  6 5r5 −13
χ_{6} 1  3 5 −3  6  0 −6 −9  3
χ_{7} 1 −3 5 −3 −6  0 −6  9  3
χ_{8} 1  1 −3 −3 −6  8  2 −3  3
χ_{9} 1 −1 −3 −3  6 −8  2  3  3

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