Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1228$ | |
| 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)(3,4)(9,12,10,11), (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 20, $C_2^3$ x 15 16: $D_4\times C_2$ x 30, $C_2^4$ 32: $C_2^2 \wr C_2$ x 8, $C_2^3 : D_4 $ x 2, $C_2^2 \times D_4$ x 5 64: $(((C_4 \times C_2): C_2):C_2):C_2$ x 8, 16T87, 16T105 x 2, 16T109 x 4 128: 16T245 x 4, 32T1237 256: 16T531 x 2, 16T536 512: 32T13404 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
16T1180 x 8, 16T1228 x 3, 16T1234 x 4, 32T36058 x 8, 32T36059 x 4, 32T36060 x 4, 32T36061 x 4, 32T36062 x 4, 32T36063 x 4, 32T36064 x 4, 32T36447 x 2, 32T36448 x 2, 32T36449 x 4, 32T36450 x 4, 32T36451 x 2, 32T36452 x 4, 32T36453 x 2, 32T36454 x 2, 32T36455 x 4, 32T36456 x 2, 32T36507 x 2, 32T36508 x 2, 32T36509 x 2, 32T36510 x 2, 32T36511 x 2, 32T36512 x 2, 32T51253 x 2, 32T52392 x 2, 32T52398 x 2, 32T52436 x 2, 32T52437 x 2, 32T52442 x 2, 32T52443 x 2, 32T55499 x 2, 32T55505 x 2, 32T64483 x 2, 32T64563 x 2, 32T70252, 32T70255, 32T85214 x 2, 32T85235 x 2, 32T86551, 32T88763, 32T88765, 32T96658Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 61 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. |