Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1849$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,3,13)(2,4,14)(5,9,12,6,10,11)(7,8), (1,10,2,9)(3,8,6,12,16,13)(4,7,5,11,15,14), (1,7,5,4,9,16,14,11,2,8,6,3,10,15,13,12) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ 12: $D_{6}$ 24: $S_4$ x 3 48: $S_4\times C_2$ x 3 96: $V_4^2:S_3$ 192: $Q_8:S_4$ x 2, $V_4^2:(S_3\times C_2)$ x 2, 12T100 384: $C_2 \wr S_4$ x 2, 16T741 768: 16T1068 1536: 24T3296, 24T3382 x 2 3072: 16T1537 6144: 32T398626 24576: 48T? Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: $S_4$
Degree 8: $Q_8:S_4$
Low degree siblings
16T1847 x 4, 16T1849 x 3, 32T1515630 x 2, 32T1515631 x 2, 32T1515632 x 2, 32T1515633 x 4, 32T1515634 x 2, 32T1515635 x 2, 32T1515636 x 2, 32T1515644 x 2, 32T1515645 x 2, 32T1515646 x 2, 32T1515647 x 2, 32T1515648 x 2, 32T1515649 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 104 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $49152=2^{14} \cdot 3$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |