Group action invariants
| Degree $n$: | $16$ | |
| Transitive number $t$: | $1664$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $4$ | |
| Generators: | (1,9,3,12)(2,10,4,11)(13,16)(14,15), (1,15,8,10,3,13,6,11)(2,16,7,9,4,14,5,12), (1,15,8,12)(2,16,7,11)(3,13,6,9)(4,14,5,10) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 7 $4$: $C_2^2$ x 7 $6$: $S_3$ $8$: $C_2^3$ $12$: $D_{6}$ x 3 $24$: $S_4$, $S_3 \times C_2^2$ $48$: $S_4\times C_2$ x 3 $96$: 12T48 $192$: $V_4^2:(S_3\times C_2)$ x 3 $384$: $C_2 \wr S_4$ x 6, 12T136 x 3 $768$: 16T1045 x 3 $1536$: 24T4591 $3072$: 24T5576 x 3 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 4: $S_4$
Degree 8: $C_2 \wr S_4$ x 3
Low degree siblings
16T1664 x 63, 32T397419 x 16, 32T397420 x 48, 32T397421 x 48Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 105 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $6144=2^{11} \cdot 3$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |