Group action invariants
| Degree $n$ : | $18$ | |
| Transitive number $t$ : | $839$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,2)(3,18,4,17)(5,6)(7,9,8,10)(11,13,15,12,14,16), (1,17,4,2,18,3)(11,14,15)(12,13,16), (1,5,13,2,6,14)(3,7,11,4,8,12)(9,16,18)(10,15,17) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $C_6$ 12: $A_4$ x 5 24: $A_4\times C_2$ x 5 48: $C_2^4:C_3$ 96: 12T56 324: $((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ 648: 18T199 1296: 18T322 2592: 18T400 20736: 12T284 41472: 18T699 82944: 18T786 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: $C_3$
Degree 6: None
Low degree siblings
18T839 x 11Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 192 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $165888=2^{11} \cdot 3^{4}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |