Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1202$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $4$ | |
| Generators: | (1,14)(2,13)(3,15)(4,16)(5,9,6,10)(7,11,8,12), (1,10,3,12,2,9,4,11)(5,13)(6,14)(7,16)(8,15), (1,7,3,6,2,8,4,5)(9,14,12,16,10,13,11,15) | |
| $|\Aut(F/K)|$: | $4$ |
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: $C_4\wr C_2$ x 6, $C_2^2 \wr C_2$ x 4, $C_2 \times (C_2^2:C_4)$ x 3 64: $(C_4^2 : C_2):C_2$ x 3, $(((C_4 \times C_2): C_2):C_2):C_2$, 16T79, 16T106 x 3, 16T111 x 3, 16T138 x 3, 16T146 128: 32T1151, 32T1153 x 3, 32T1154 x 3 256: 16T500 x 3, 64T? x 4 512: 128T? Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
Degree 8: $(((C_4 \times C_2): C_2):C_2):C_2$
Low degree siblings
16T1202 x 15, 32T36265 x 24, 32T36266 x 24, 32T36267 x 8, 32T56437 x 24Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 106 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. |