M_{12}

3^{2}.2.S_{4} 220 1a + 11a + 54a + 55a + 99a 5

Character Numbers: [ 1, 2, 7, 8, 12 ]

3^{2}.2.S_{4} 220 1a + 11b + 54a + 55a + 99a 5

Character Numbers: [ 1, 3, 7, 8, 12 ]

S_{1} S_{2} S_{3} S_{4} S_{5}
χ_{1} 1 12 27 72 108
χ_{2} 1 −4 15 −24 12
χ_{3} 1 1 5  6 −13
χ_{4} 1 5 −3 −6  3
χ_{5} 1 −3 −3  2  3

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