Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $879$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,4,17)(2,3,18)(7,8)(9,10)(11,16,14,12,15,13), (1,6,14)(2,5,13)(3,9,15,4,10,16)(7,12,18,8,11,17), (1,14,5)(2,13,6)(3,15,10,17,11,8)(4,16,9,18,12,7) | |
| $|\Aut(F/K)|$: | $2$ |
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: $A_4$ x 5, $C_6\times C_2$ 24: $A_4\times C_2$ x 15 48: $C_2^2 \times A_4$ x 5, $C_2^4:C_3$ 96: 12T56 x 3 192: 12T90 648: $S_3 \wr C_3 $ 1296: 18T283 2592: 18T399 5184: 18T472 41472: 12T292 82944: 18T765 165888: 18T838 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $C_3$
Degree 6: None
Degree 9: $S_3 \wr C_3 $
Low degree siblings
18T879 x 23Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 360 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $331776=2^{12} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |