Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $951$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,13,9,2,14,8)(3,15,7)(4,18)(5,16,6,17)(10,11), (1,14,2,13)(3,15)(4,12)(5,10)(6,11)(7,8,9), (1,10,14,16,9,5,3,11,15,18,7,6)(2,12,13,17,8,4) | |
| $|\Aut(F/K)|$: | $1$ |
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 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 3: None
Degree 6: $C_3^2:D_4$
Degree 9: None
Low degree siblings
There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 275 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $3359232=2^{9} \cdot 3^{8}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |