Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1781$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $7$ | |
| Generators: | (1,3,5,16)(2,4,6,15)(7,9,11,14)(8,10,12,13), (1,2)(3,12,4,11)(13,14), (1,9)(2,10)(5,6)(11,12)(13,14), (3,15)(4,16)(7,12,8,11)(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 8, 16T87, 16T105 x 2, 16T109 x 4 128: $C_2 \wr C_2\wr C_2$ x 4, 16T245 x 4, 32T1237 256: 16T477 x 2, 16T509 x 2, 16T531 x 2, 16T536 512: 32T12264 x 2, 32T13404 1024: 16T1116, 16T1124 x 2 2048: 32T101073 4096: 16T1553 8192: 32T519899 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
16T1781 x 31, 32T724047 x 16, 32T724048 x 16, 32T724049 x 16, 32T724050 x 16, 32T724051 x 16, 32T724052 x 16, 32T724053 x 16, 32T724054 x 16, 32T724055 x 16, 32T724056 x 16, 32T724057 x 16, 32T724058 x 16, 32T724059 x 16, 32T724060 x 16, 32T724061 x 16, 32T724062 x 16, 32T724063 x 16, 32T724064 x 16, 32T724065 x 16, 32T724066 x 16, 32T724067 x 16, 32T724068 x 16, 32T724069 x 16, 32T724070 x 16, 32T724071 x 16, 32T724072 x 16, 32T724073 x 16, 32T724074 x 16, 32T724075 x 16, 32T724076 x 16, 32T724077 x 16, 32T728316 x 16, 32T742128 x 8, 32T742551 x 8, 32T742699 x 8, 32T873165 x 8, 32T873614 x 8, 32T968056 x 8, 32T968148 x 8, 32T1037996 x 8, 32T1038045 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 148 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $16384=2^{14}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |