Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $790$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $4$ | |
| Generators: | (1,2)(3,4)(5,6)(7,8)(9,13,10,14)(11,16,12,15), (1,5)(2,6)(3,8)(4,7)(9,10)(15,16), (9,10)(11,12)(13,14)(15,16), (1,4,2,3)(5,7,6,8), (1,9)(2,10)(3,11,4,12)(5,13)(6,14)(7,16,8,15) | |
| $|\Aut(F/K)|$: | $2$ |
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 4: $D_{4}$ x 3
Degree 8: $C_2^2 \wr C_2$
Low degree siblings
16T790 x 23, 32T9670 x 24, 32T9671 x 24, 32T9672 x 12, 32T9673 x 12, 32T9674 x 24, 32T9675 x 24, 32T9676 x 24, 32T9677 x 12, 32T9678 x 24Siblings 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, 400856] |
| Character table: Data not available. |