Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1574$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $6$ | |
| Generators: | (1,8,16,12,4,5,13,10,2,7,15,11,3,6,14,9), (1,10,16,5,2,9,15,6)(3,11,13,8,4,12,14,7), (1,5,4,7)(2,6,3,8)(9,15,12,13)(10,16,11,14) | |
| $|\Aut(F/K)|$: | $2$ |
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: $C_2 \wr C_2\wr C_2$ x 4, 16T227 x 2, 16T240, 32T1151 x 2 256: 16T482 x 2, 16T502, 16T532, 16T542 x 2, 16T543 512: 32T12349 x 2, 32T13346 1024: 16T1174 2048: 32T159726 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 8: $C_2 \wr C_2\wr C_2$
Low degree siblings
16T1574 x 15, 32T207258 x 8, 32T207259 x 8, 32T207260 x 8, 32T207261 x 8, 32T207262 x 8, 32T207263 x 8, 32T207264 x 8, 32T207265 x 8, 32T207266 x 8, 32T207267 x 8, 32T207268 x 8, 32T207269 x 8, 32T207270 x 8, 32T207271 x 8, 32T207272 x 8, 32T220820 x 8, 32T249207 x 4, 32T249319 x 4, 32T249364 x 4, 32T311708 x 4, 32T313974 x 4, 32T314000 x 4, 32T314001 x 4, 32T314022 x 4, 32T314232 x 4Siblings 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: | $4096=2^{12}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |