Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1558$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $6$ | |
| Generators: | (1,3,5,7,2,4,6,8)(9,10)(11,12), (1,9,5,13,2,10,6,14)(3,12,7,15,4,11,8,16), (1,7,2,8)(3,5,4,6)(9,15,10,16)(11,14,12,13), (9,10)(13,14), (1,7,2,8)(3,6,4,5)(9,13)(10,14)(11,12) | |
| $|\Aut(F/K)|$: | $2$ |
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: $(C_4^2 : C_2):C_2$ x 4, $(((C_4 \times C_2): C_2):C_2):C_2$ x 4, 16T87, 16T105 x 2, 16T109 x 4 128: $C_2 \wr C_2\wr C_2$ x 4, 16T245 x 2, 16T265 x 2, 32T1237 256: 16T477 x 2, 16T509 x 2, 16T511, 16T531, 16T538 512: 32T12264 x 2, 32T12969 1024: 16T1177 2048: 32T128071 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 8: $(C_4^2 : C_2):C_2$
Low degree siblings
16T1558 x 15, 32T207027 x 8, 32T207028 x 16, 32T207029 x 8, 32T207030 x 8, 32T207031 x 16, 32T207032 x 8, 32T207033 x 16, 32T207034 x 8, 32T207035 x 16, 32T207036 x 8, 32T207037 x 8, 32T220698 x 8, 32T245897 x 4, 32T245952 x 8, 32T303536 x 8, 32T327819 x 4, 32T327841 x 4, 32T375037 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 94 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. |