Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $797$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $4$ | |
| Generators: | (1,6)(2,5)(3,7)(4,8)(9,14)(10,13)(11,16)(12,15), (1,8,2,7)(3,6,4,5)(9,12,10,11)(13,15,14,16), (9,10)(13,14), (1,16,4,9)(2,15,3,10)(5,11,7,14)(6,12,8,13) | |
| $|\Aut(F/K)|$: | $2$ |
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: 16T199 x 2, 32T1149 256: 32T3478 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 3
Degree 8: $C_4\times C_2$
Low degree siblings
16T785 x 8, 16T787 x 4, 16T791 x 8, 16T797 x 3, 32T9617 x 16, 32T9618 x 8, 32T9619 x 8, 32T9620 x 8, 32T9621 x 4, 32T9622 x 8, 32T9623 x 8, 32T9624 x 4, 32T9625 x 8, 32T9640 x 4, 32T9641 x 8, 32T9642 x 2, 32T9643 x 4, 32T9644 x 4, 32T9645 x 2, 32T9646 x 4, 32T9679 x 8, 32T9680 x 8, 32T9681 x 8, 32T9682 x 4, 32T9683 x 8, 32T9684 x 4, 32T9685 x 4, 32T9686 x 4, 32T9687 x 4, 32T9688 x 4, 32T9726 x 2, 32T9727 x 16, 32T9728 x 4, 32T9729 x 2, 32T9730 x 8, 32T9731 x 4, 32T9732 x 4, 32T9733 x 8, 32T9734 x 4, 32T9735 x 4, 32T19793 x 4Siblings 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, 400670] |
| Character table: Data not available. |