M_{22}.2

{2^{4} : S_{5} ≤ 2^{5} : \atop S_{5}} 462 1a^{±} + 21a^{±} + 55a^{±} + 154a^{±} 8

Character Numbers: [ 1, 2, 3, 4, 9, 10, 13, 14 ]

S_{1} S_{2} S_{3} S_{4} S_{5} S_{6}  S_{7} S_{8}
χ_{1} 1 1 30 30 40 40 160 160
χ_{2} 1 −1 −30 30 −40 40 −160 160
χ_{3} 1 1 −3 −3 18 18 −16 −16
χ_{4} 1 −1 3 −3 −18 18 16 −16
χ_{5} 1 1  9 9 −2 −2 −8 −8
χ_{6} 1 −1 −9 9  2 −2  8 −8
χ_{7} 1 1 −3 −3 −2 −2  4  4
χ_{8} 1 −1  3 −3  2 −2 −4  4

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