Degree 12: T₁₆₈

Name(s): [3^4:2]E(4)

Order: 648 = 2³ · 3⁴

Parity: 1

|Aut(K)|=|C_S12(G)|= 1

Subfields: 2T1, 2T1, 2T1, 4T2

Other representations: 12T168, 18T193, 18T193, 18T193, 18T193, 18T193, 18T193

Resolvents
  2: 2T1, 2T1, 2T1, 2T1, 2T1, 2T1, 2T1
  4: 4T2, 4T2, 4T2, 4T2, 4T2, 4T2, 4T2
  6: 3T2, 3T2, 3T2, 3T2
  8: 8T3
  12: 6T3, 6T3, 6T3, 6T3, 6T3, 6T3, 6T3, 6T3, 6T3, 6T3, 6T3, 6T3
  24: 12T10, 12T10, 12T10, 12T10
  36: 6T9, 6T9, 6T9, 6T9, 6T9, 6T9
  72: 12T37, 12T37, 12T37, 12T37, 12T37, 12T37
  216: 12T117, 12T117, 12T117, 12T117