Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1759$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,5,3,15)(2,6,4,16)(7,9,13,12,8,10,14,11), (3,6,4,5)(7,10,8,9)(11,12)(13,14), (1,9,16,12,4,14,2,10,15,11,3,13)(5,7,6,8) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 6: $S_3$ 8: $D_{4}$ x 2, $C_2^3$ 12: $D_{6}$ x 3 16: $D_4\times C_2$ 24: $S_4$, $S_3 \times C_2^2$ 48: $S_4\times C_2$ x 3, 12T28 96: 12T48 192: $V_4^2:(S_3\times C_2)$, 12T86 384: $C_2 \wr S_4$ x 2, 12T136 768: 12T186, 16T1045, 16T1049 1536: 32T96912 3072: 16T1519 6144: 24T8319 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $S_4$
Degree 8: $S_4\times C_2$
Low degree siblings
16T1757 x 8, 16T1759 x 7, 32T720583 x 8, 32T720584 x 4, 32T720585 x 4, 32T720586 x 4, 32T720587 x 4, 32T720588 x 4, 32T720589 x 4, 32T720597 x 4, 32T720598 x 4, 32T720599 x 4, 32T720600 x 4, 32T720601 x 4, 32T720602 x 4, 32T720603 x 4, 32T720604 x 4, 32T720605 x 4, 32T720606 x 4, 32T720607 x 4, 32T720608 x 4, 32T720609 x 4, 32T720610 x 4, 32T720882 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 93 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $12288=2^{12} \cdot 3$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |