Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1192$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $6$ | |
| Generators: | (1,14,7,10,2,13,8,9)(3,15,6,12,4,16,5,11), (1,5,2,6)(3,7,4,8)(9,15,12,14,10,16,11,13) | |
| $|\Aut(F/K)|$: | $4$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_4$ x 6, $C_2^2$ 8: $D_{4}$ x 3, $C_4\times C_2$ x 3, $Q_8$ 16: $C_2^2:C_4$ x 3, $C_4^2$, $C_4:C_4$ x 3 32: $C_4\wr C_2$ x 2, $C_2^3 : C_4 $ x 2, 32T41 64: $((C_8 : C_2):C_2):C_2$, $(((C_4 \times C_2): C_2):C_2):C_2$, 16T74, 16T77, 16T121, 16T140, 16T154 128: 32T1095, 32T1311, 32T1313 256: 16T521, 16T563, 16T590 512: 32T13179 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $C_4$
Degree 8: $((C_8 : C_2):C_2):C_2$
Low degree siblings
16T1192 x 15, 32T36166 x 8, 32T36167 x 8, 32T36168 x 16, 32T36169 x 16, 32T36170 x 8, 32T56480 x 8Siblings 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. |