M_{12}.2

M_{8}.(S_{4} × 2) 495 1a^{+} + 11ab + 54a^{±} + 55a^{+} + 66a^{+} + 99a^{−}

+ 144a^{+}

8

Character Numbers: [ 1, 3, 7, 8, 9, 12, 15, 18 ]

S_{1}  S_{2}  S_{3}  S_{4}  S_{5} S_{6}  S_{7}  S_{8}
χ_{1} 1  6  16  24  64 96  96  192
χ_{2} 1  −3  −8  6  16 −12  24  −24
χ_{3} 1 2 − r5 2 + 2r5 1 − 3r5 6 + 2r5  8 −6 + 2r5 −14 − 2r5
χ_{4} 1 2 + r5 −4b5 1 + 3r5 6 − 2r5  8 −6 − 2r5 −14 + 2r5
χ_{5} 1  −3  4  6  4 −12  −12  12
χ_{6} 1  3  4  0  −8 −12  12  0
χ_{7} 1  1  −4  −6  4 −4  −4  12
χ_{8} 1  −2  −1  0  −8  8  2  0

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