M_{12}

3^{2} : 2.A_{4} ≤ 3^{2}.2.S_{4} 440 1a + 11a + 45a + 54a + 55ac + 99a + 120a

8

Character Numbers: [ 1, 2, 6, 7, 8, 10, 12, 13 ]

3^{2} : 2.A_{4} ≤ 3^{2}.2.S_{4} 440 1a + 11b + 45a + 54a + 55ab + 99a + 120a

8

Character Numbers: [ 1, 3, 6, 7, 8, 9, 12, 13 ]

S_{1} S_{2} S_{3} S_{4} S_{5} S_{6} S_{7} S_{8}
χ_{1} 1 1 24 27 27 72 72 216
χ_{2} 1 1 −8 15 15 −24 −24 24
χ_{3} 1 −1 0 3 −3 16 −16  0
χ_{4} 1 1 2 5 5 6 6 −26
χ_{5} 1 1 10 −3 −3 −6 −6  6
χ_{6} 1 −1 0 −9 9  0  0  0
χ_{7} 1 1 −6 −3 −3  2  2  6
χ_{8} 1 −1 0 3 −3 −6  6  0

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