M_{24}

{L_{3}(4).3 ≤ \atop L_{3}(4).3.2_{2}} 4048 {1a + 23a + 252a + 253a + 483a + 1265a \atop + 1771a} 7

Character Numbers: [ 1, 2, 7, 8, 9, 17, 18 ]

S_{1} S_{2} S_{3} S_{4} S_{5} S_{6}  S_{7}
χ_{1} 1 1 63 63 420 1260 2240
χ_{2} 1 1 39 39 −60 300 −320
χ_{3} 1 1 17 17  6 −74  32
χ_{4} 1 −1 −21 21  0  0  0
χ_{5} 1 1 −3 −3 46  6 −48
χ_{6} 1 1 −3 −3 −18  6  16
χ_{7} 1 −1  3 −3  0  0  0

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