Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1888$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,12,2,11)(3,8,4,7)(5,10,15,13)(6,9,16,14), (3,5,15,4,6,16)(7,8)(9,11)(10,12)(13,14) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_4$ x 2, $C_2^2$ 8: $D_{4}$ x 2, $C_4\times C_2$ 16: $C_2^2:C_4$ 72: $C_3^2:D_4$ 144: 12T79 1152: $S_4\wr C_2$ 2304: 12T237 36864: 16T1826 73728: 32T1832106 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: None
Degree 8: $S_4\wr C_2$
Low degree siblings
16T1888 x 7, 32T2076214 x 4, 32T2076215 x 4, 32T2076216 x 4, 32T2076217 x 4, 32T2076218 x 4, 32T2076219 x 4, 32T2076220 x 4, 32T2076340 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 130 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $147456=2^{14} \cdot 3^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |