Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1127$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $5$ | |
| Generators: | (1,12,2,11)(3,10,4,9)(5,15)(6,16)(7,14)(8,13), (1,11)(2,12)(3,10)(4,9)(7,8)(13,14), (9,10)(11,12)(13,14)(15,16), (1,5)(2,6)(3,7)(4,8)(9,16)(10,15)(11,14)(12,13), (1,4)(2,3)(5,7)(6,8)(11,12)(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 4, 16T87, 16T105 x 2, 16T109 x 4 128: 16T245 x 2, 32T1237 256: 16T479 x 2, 16T531 512: 32T12299 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 8: $(((C_4 \times C_2): C_2):C_2):C_2$
Low degree siblings
16T1127 x 15, 32T35632 x 8, 32T35633 x 16, 32T35634 x 32, 32T35635 x 8, 32T35636 x 16, 32T35637 x 8, 32T35638 x 16, 32T35639 x 16, 32T46317 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. |