Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1848$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,11)(2,12)(5,16,7,14,6,15,8,13), (1,9,15,7,2,10,16,8)(3,14,6,12,4,13,5,11) | |
| $|\Aut(F/K)|$: | $2$ |
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: $C_2^3:S_4$ x 2, $V_4^2:(S_3\times C_2)$ x 2, 12T100 384: $C_2 \wr S_4$ x 2, 16T747 768: 16T1068 1536: 24T3293, 24T3382 x 2 3072: 16T1521 x 2, 16T1538 6144: 32T397650 24576: 48T? Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: $S_4$
Degree 8: $C_2^3:S_4$
Low degree siblings
16T1848 x 3, 16T1852 x 4, 32T1515637 x 2, 32T1515638 x 2, 32T1515639 x 4, 32T1515640 x 2, 32T1515641 x 2, 32T1515642 x 2, 32T1515643 x 2, 32T1515664 x 2, 32T1515665 x 2, 32T1515666 x 2, 32T1515667 x 2, 32T1515668 x 2, 32T1515669 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 116 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. |