Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $781$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $4$ | |
| Generators: | (1,2)(3,4), (1,10,3,12)(2,9,4,11)(5,14,8,15)(6,13,7,16), (5,12)(6,11)(7,9)(8,10), (9,10)(11,12)(13,14)(15,16), (1,5,3,7)(2,6,4,8)(9,14,12,15)(10,13,11,16) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 15 4: $C_4$ x 8, $C_2^2$ x 35 8: $D_{4}$ x 24, $C_4\times C_2$ x 28, $C_2^3$ x 15 16: $D_4\times C_2$ x 36, $C_2^2:C_4$ x 48, $C_4\times C_2^2$ x 14, $C_2^4$ 32: $C_2^2 \wr C_2$ x 16, $C_2 \times (C_2^2:C_4)$ x 36, $C_2^2 \times D_4$ x 6, 32T34 64: 16T79 x 8, 16T105 x 4, 32T262 x 3 128: 16T241 x 2, 32T1149 256: 32T4207 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 8: $C_2^2:C_4$
Low degree siblings
16T781 x 7, 16T786 x 8, 16T799 x 8, 32T9579 x 8, 32T9580 x 4, 32T9581 x 4, 32T9582 x 4, 32T9583 x 8, 32T9584 x 4, 32T9585 x 4, 32T9586 x 4, 32T9587 x 4, 32T9588 x 4, 32T9589 x 4, 32T9590 x 4, 32T9591 x 4, 32T9592 x 4, 32T9593 x 4, 32T9626 x 4, 32T9627 x 4, 32T9628 x 4, 32T9629 x 4, 32T9630 x 4, 32T9631 x 4, 32T9632 x 8, 32T9633 x 4, 32T9634 x 4, 32T9635 x 4, 32T9636 x 4, 32T9637 x 4, 32T9638 x 4, 32T9639 x 4, 32T9744 x 4, 32T9745 x 4, 32T9746 x 4, 32T9747 x 4, 32T9748 x 4, 32T9749 x 4, 32T9750 x 4, 32T9751 x 4, 32T9752 x 4, 32T9753 x 4, 32T9754 x 4, 32T9755 x 4, 32T9756 x 4, 32T21967 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 62 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $512=2^{9}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [512, 400831] |
| Character table: Data not available. |