Degree 12: T₂₅₀

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

Order: 3072 = 2¹⁰ · 3

Parity: -1

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

Subfields: 3T2, 6T11

Other representations: 12T250, 12T250, 12T250, 12T250, 12T250, 12T250, 12T250, 12T250, 12T250, 12T250, 12T250, 12T250, 12T250, 12T250, 12T250

Resolvents
  2: 2T1, 2T1, 2T1, 2T1, 2T1, 2T1, 2T1
  4: 4T2, 4T2, 4T2, 4T2, 4T2, 4T2, 4T2
  6: 3T2
  8: 8T3
  12: 6T3, 6T3, 6T3
  24: 4T5, 4T5, 4T5, 12T10
  48: 6T11, 6T11, 6T11, 6T11, 6T11, 6T11, 6T11, 6T11, 6T11
  96: 8T34, 12T48, 12T48, 12T48
  192: 12T100, 12T100, 12T100
  384: 12T139
  768: 16T1055
  1536: 24T3386