Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1220$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $4$ | |
| Generators: | (1,8)(2,7)(3,4)(9,12,10,11), (1,5,2,6)(3,7)(4,8)(9,13,10,14)(11,16)(12,15), (1,14,8,16,2,13,7,15)(3,10,5,11,4,9,6,12), (9,10)(13,14) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 15 4: $C_2^2$ x 35 8: $D_{4}$ x 12, $C_2^3$ x 15 16: $D_4\times C_2$ x 18, $Q_8:C_2$ x 4, $C_2^4$ 32: $C_2^2 \wr C_2$ x 4, $C_2^3 : D_4 $ x 2, $C_2 \times (C_4\times C_2):C_2$ x 2, $C_2^2 \times D_4$ x 3 64: $(((C_4 \times C_2): C_2):C_2):C_2$ x 4, 16T73, 16T105, 16T115 x 4, 16T117 128: 16T245 x 2, 32T1074 256: 16T473, 16T494 x 2 512: 32T15122 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$, $D_{4}$ x 2
Degree 8: $D_4\times C_2$
Low degree siblings
16T1129 x 8, 16T1159 x 4, 16T1220 x 3, 32T35645 x 8, 32T35646 x 4, 32T35647 x 4, 32T35648 x 4, 32T35649 x 4, 32T35650 x 4, 32T35651 x 4, 32T35868 x 4, 32T35869 x 2, 32T35870 x 2, 32T35871 x 2, 32T35872 x 2, 32T35873 x 2, 32T35874 x 2, 32T36375 x 2, 32T36376 x 2, 32T36377 x 4, 32T36378 x 2, 32T36379 x 4, 32T36380 x 2, 32T36381 x 2, 32T36382 x 4, 32T36383 x 2, 32T51746 x 2, 32T51748 x 2, 32T52422 x 2, 32T52428 x 2, 32T54838 x 2, 32T54839 x 2, 32T55510 x 2, 32T55519 x 2, 32T55626 x 2, 32T64557 x 2, 32T64573 x 2, 32T71209, 32T71271, 32T85202 x 2, 32T85223 x 2, 32T86555, 32T88757, 32T88829, 32T96660Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 55 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1024=2^{10}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |