Degree 12: T₂₂₂

Name(s): [D(4)^4]3=D(4)wr3

Order: 1536 = 2⁹ · 3

Parity: -1

|Aut(K)|=|C_S12(G)|= 2

Subfields: 3T1, 6T6

Other representations: 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222, 12T222

Resolvents
  2: 2T1, 2T1, 2T1
  3: 3T1
  4: 4T2
  6: 6T1, 6T1, 6T1
  12: 4T4, 4T4, 4T4, 4T4, 4T4, 12T2
  24: 6T6, 6T6, 6T6, 6T6, 6T6, 6T6, 6T6, 6T6, 6T6, 6T6, 6T6, 6T6, 6T6, 6T6, 6T6
  48: 12T25, 12T25, 12T25, 12T25, 12T25, 12T32
  96: 12T56, 12T56, 12T56
  192: 12T90
  384: 16T718
  768: 24T1654