Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1230$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $5$ | |
| Generators: | (1,16)(2,15)(3,13,4,14)(5,9,7,11)(6,10,8,12), (1,10,4,12,2,9,3,11)(5,14,7,15,6,13,8,16), (1,8,2,7)(3,6,4,5)(9,15,11,14,10,16,12,13) | |
| $|\Aut(F/K)|$: | $2$ |
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 4, $C_2 \times (C_2^2:C_4)$ x 3 64: $((C_8 : C_2):C_2):C_2$ x 4, $(((C_4 \times C_2): C_2):C_2):C_2$ x 2, 16T76 x 2, 16T79, 16T146 x 2 128: 16T227 x 2, 16T240, 32T1151 x 2 256: 16T502, 16T532, 16T543 512: 64T? Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
Degree 8: $C_2^3: C_4$
Low degree siblings
16T1230 x 15, 32T36481 x 8, 32T36482 x 64, 32T36483 x 8, 32T36484 x 8, 32T36485 x 8, 32T36486 x 8, 32T36487 x 8, 32T36488 x 8, 32T48754 x 8, 32T50083 x 8, 32T50680 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 58 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. |