Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1845$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,7,6,9,16,13,2,8,5,10,15,14)(3,12)(4,11), (1,11,5,10,4,13)(2,12,6,9,3,14) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 3: $C_3$ 4: $C_2^2$ 6: $C_6$ x 3 12: $A_4$, $C_6\times C_2$ 24: $A_4\times C_2$ x 3 48: $C_2^2 \times A_4$ 96: $C_2^4:C_6$ x 3 192: $C_2\wr A_4$ x 6, 12T87 x 3, 16T417 x 2 384: 16T722 x 3 768: 24T2232 1536: 24T3049 x 3 3072: 16T1515 6144: 32T398882 24576: 48T? Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: $A_4$
Degree 8: $C_2\wr A_4$
Low degree siblings
16T1845 x 7, 32T1515616 x 4, 32T1515617 x 4, 32T1515618 x 4, 32T1515619 x 4, 32T1515620 x 4, 32T1515621 x 4, 32T1515622 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 140 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. |