M_{12}.2

4^{2} : D_{12}.2 495 1a^{+} + 16ab + 45a^{−} + 54a^{±} + 66a^{+} + 99a^{−}

+ 144a^{+}

8

Character Numbers: [ 1, 4, 6, 7, 8, 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  7  6  10  −21 −12  12
χ_{3} 1  −3  −4  6  −12  12 −12  12
χ_{4} 1 2 + r5 −4b5 1 + 3r5 −8 + 4b5 −6 − 2r5  8 −4b5
χ_{5} 1 2 − r5 2 + 2r5 1 − 3r5 −10 − 2r5 −6 + 2r5  8 2 + 2r5
χ_{6} 1  3  4  0  4  12 −12  −12
χ_{7} 1  1  −4  −6  4  −4 −4  12
χ_{8} 1  −2  −1  0  4  2  8  −12

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, 6, 7, 8 ], [ 2, 3, 4, 5, 6, 8 ], [ 2, 3, 4, 5, 7 ], [ 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, 6, 8 ], [ 2, 3, 4, 7 ], [ 2, 3, 4, 7, 8 ], [ 2, 3, 4, 8 ], [ 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 ], [ 2, 3, 6, 7 ], [ 2, 3, 6, 7, 8 ], [ 2, 3, 6, 8 ], [ 2, 3, 7 ], [ 2, 3, 7, 8 ], [ 2, 3, 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 ], [ 2, 4, 5, 7, 8 ], [ 2, 4, 5, 8 ], [ 2, 4, 6 ], [ 2, 4, 6, 7, 8 ], [ 2, 4, 6, 8 ], [ 2, 4, 7 ], [ 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, 7, 8 ], [ 2, 6, 8 ], [ 2, 7 ], [ 2, 7, 8 ], [ 2, 8 ], [ 3 ], [ 3, 4, 5, 6 ], [ 3, 4, 5, 6, 7 ], [ 3, 4, 5, 6, 7, 8 ], [ 3, 4, 5, 6, 8 ], [ 3, 4, 5, 7 ], [ 3, 4, 5, 7, 8 ], [ 3, 4, 6 ], [ 3, 4, 6, 7 ], [ 3, 4, 6, 7, 8 ], [ 3, 4, 6, 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, 6, 8 ], [ 3, 7 ], [ 3, 7, 8 ], [ 3, 8 ], [ 4 ], [ 4, 5 ], [ 4, 5, 6 ], [ 4, 5, 6, 7 ], [ 4, 5, 6, 7, 8 ], [ 4, 5, 6, 8 ], [ 4, 5, 7 ], [ 4, 5, 7, 8 ], [ 4, 5, 8 ], [ 4, 6 ], [ 4, 6, 7 ], [ 4, 6, 7, 8 ], [ 4, 6, 8 ], [ 4, 7 ], [ 4, 7, 8 ], [ 4, 8 ], [ 5 ], [ 5, 6 ], [ 5, 6, 7 ], [ 5, 6, 7, 8 ], [ 5, 6, 8 ], [ 5, 7 ], [ 5, 7, 8 ], [ 5, 8 ], [ 6, 7, 8 ], [ 6, 8 ], [ 7 ], [ 7, 8 ], [ 8 ]

2