Sextic Fields

We separate new fields from old fields.

Warning we have not checked that these lists are complete with respect to new solvable fields (Galois groups C₃².C₄ and C₃².D₄). One should take these results with an extra grain of salt.

Fields are organized by the set S. We start with cases where S contains one prime.

• S={2} No fields.
• S={3}
  • 3 old fields: gp dvi
  • No new fields.
• S={5} No fields.
• S={7}
  • 1 old field: gp dvi
  • No new fields.
• S={11} No fields.
• S={13}
  • 1 old field: gp dvi
  • No new fields.
• S={17} No fields.
• S={19}
  • 1 old field: gp dvi
  • No new fields.

• S={2,3}
  • 279 old fields: gp dvi
  • 116 new fields: gp dvi
• S={2,5}
  • 74 old fields: gp dvi
  • 32 new fields: gp dvi
• S={3,5}
  • 56 old fields: gp dvi
  • 48 new fields: gp dvi
• S={2,7}
  • 16 old fields: gp dvi
  • 4 new fields: gp dvi
• S={3,7}
  • 51 old fields: gp dvi
  • 4 new fields: gp dvi
• S={5,7}
  • 10 old fields: gp dvi
  • 2 new fields: gp dvi
• S={2,11}
  • 65 old fields: gp dvi
  • 2 new fields: gp dvi
• S={3,11}
  • 47 old fields: gp dvi
  • 6 new fields: gp dvi
• S={5,11}
  • 5 old fields: gp dvi
  • 4 new fields: gp dvi
• S={7,11}
  • 3 old fields: gp dvi
  • No new fields.
• S={2,13}
  • 115 old fields: gp dvi
  • 2 new fields: gp dvi
• S={3,13}
  • 84 old fields: gp dvi
  • 10 new fields: gp dvi
• S={5,13}
  • 16 old fields: gp dvi
  • 2 new fields: gp dvi
• S={7,13}
  • 14 old fields: gp dvi
  • No new fields.
• S={11,13}
  • 10 old fields: gp dvi
  • No new fields.
• S={2,17}
  • 4 old fields: gp dvi
  • 14 new fields: gp dvi
• S={3,17}
  • 38 old fields: gp dvi
  • 10 new fields: gp dvi
• S={5,17}
  • 12 old fields: gp dvi
  • 2 new fields: gp dvi
• S={7,17}
  • 6 old fields: gp dvi
  • No new fields.
• S={11,17}
  • 11 old fields: gp dvi
  • No new fields.
• S={13,17}
  • 2 old fields: gp dvi
  • 2 new fields: gp dvi
• S={2,19}
  • 148 old fields: gp dvi
  • 2 new fields: gp dvi
• S={3,19}
  • 66 old fields: gp dvi
  • 4 new fields: gp dvi
• S={5,19}
  • 10 old fields: gp dvi
  • 6 new fields: gp dvi
• S={7,19}
  • 21 old fields: gp dvi
  • No new fields.
• S={11,19}
  • 7 old fields: gp dvi
  • No new fields.
• S={13,19}
  • 22 old fields: gp dvi
  • 2 new fields: gp dvi
• S={17,19}
  • 3 old fields: gp dvi
  • No new fields.