Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1905$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,11,3,13,16,9,2,12,4,14,15,10)(5,8)(6,7), (1,16,3)(2,15,4)(7,12,13,9,8,11,14,10), (1,3)(2,4)(5,16,6,15)(7,12,13,9,8,11,14,10) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 8: $D_{4}$ x 6, $C_2^3$ 16: $D_4\times C_2$ x 3 32: $C_2^2 \wr C_2$ 72: $C_3^2:D_4$ 144: 12T77 288: 12T125 1152: $S_4\wr C_2$ 2304: 12T235 4608: 12T260 73728: 16T1864 147456: 32T2077237 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 8: $S_4\wr C_2$
Low degree siblings
16T1905 x 15, 32T2265666 x 8, 32T2265667 x 8, 32T2265668 x 8, 32T2265669 x 8, 32T2265670 x 8, 32T2265671 x 8, 32T2265672 x 8, 32T2265673 x 8, 32T2265674 x 8, 32T2265675 x 8, 32T2265676 x 8, 32T2265677 x 8, 32T2265678 x 8, 32T2265679 x 8, 32T2265680 x 8, 32T2265730 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 230 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $294912=2^{15} \cdot 3^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |