Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1224$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $4$ | |
| Generators: | (5,8)(6,7)(9,12)(10,11)(13,16)(14,15), (1,5,2,6)(3,7,4,8)(9,13)(10,14)(11,16)(12,15), (1,9,7,16)(2,10,8,15)(3,12,5,14)(4,11,6,13) | |
| $|\Aut(F/K)|$: | $4$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_4$ x 4, $C_2^2$ x 7 8: $D_{4}$ x 12, $C_4\times C_2$ x 6, $C_2^3$ 16: $D_4\times C_2$ x 6, $C_2^2:C_4$ x 12, $C_4\times C_2^2$ 32: $C_2^2 \wr C_2$ x 4, $C_2^3 : C_4 $ x 12, $C_2 \times (C_2^2:C_4)$ x 3 64: $((C_8 : C_2):C_2):C_2$ x 24, 16T76 x 6, 16T79 128: 16T227 x 12, 16T240 x 3 256: 16T502 x 6, 16T581 512: 16T911 x 3 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $C_4$
Degree 8: $((C_8 : C_2):C_2):C_2$ x 3
Low degree siblings
16T1224 x 1023, 32T36422 x 3072, 32T36423 x 768, 32T36424 x 768, 32T36425 x 1536, 32T36426 x 6144, 32T36427 x 1536, 32T36428 x 1536, 32T36429 x 768, 32T50165 x 128Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 88 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. |