M_{24}

\begin{matrix}2^{6} : (L_{3}(2) × 3) \\ ≤ 2^{6} : (L_{3}(2) × S_{3}) \end{matrix} 7590 1a + 252a + 253a + 483a + 1035a + 1265a

+ 2024a + 2277a

8

Character Numbers: [ 1, 7, 8, 9, 14, 17, 19, 20 ]

S_{1} S_{2} S_{3} S_{4} S_{5} S_{6}  S_{7} S_{8}
χ_{1} 1 1 56 56 84 2016 2688 2688
χ_{2} 1 1 10 10 38 84 −72 −72
χ_{3} 1 −1 −14 14 0  0 −168 168
χ_{4} 1 1 −10 −10 18 −96  48 48
χ_{5} 1 1 10 10 −6 −48  16 16
χ_{6} 1 −1 10 −10 0  0 −24 24
χ_{7} 1 1 −4 −4 −6 36 −12 −12
χ_{8} 1 −1 −4  4 0  0  32 −32

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