M_{12}.2

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

Character Numbers: [ 1, 2, 3, 7, 8, 12, 13 ]

S_{1} S_{2}  S_{3}  S_{4} S_{5}  S_{6} S_{7}
χ_{1} 1 1  36  36 40  60 90
χ_{2} 1 1 −36 −36 40 −60 90
χ_{3} 1 1 0 0 16 0 −18
χ_{4} 1 1 −2r5 −2r5 −4 4r5  2
χ_{5} 1 1 2r5 2r5 −4 −4r5  2
χ_{6} 1 −1 −6  6 0  0  0
χ_{7} 1 −1  6 −6 0  0  0

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