M_{12}.2

(2^{2} × A_{5}).2 396 {1a^{+} + 16ab + 45a^{+} + 54a^{±} + 66a^{+} + \atop 144a^{+}} 7

Character Numbers: [ 1, 4, 5, 7, 8, 12, 18 ]

S_{1}  S_{2} S_{3}  S_{4}  S_{5} S_{6}  S_{7}
χ_{1} 1  15 20  60  60 120  120
χ_{2} 1  6 −7  15  −12  3  −6
χ_{3} 1  −5 4  4  −12 −8  16
χ_{4} 1 1 + 2r5 −2 −4r5 8 − 2r5 −12 4 + 4r5
χ_{5} 1 1 − 2r5 −2 4r5 8 + 2r5 −12 −8b5
χ_{6} 1  3 8  0  0  0  −12
χ_{7} 1  −2 −2 −5  0 10  −2

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