Group action invariants
| Degree $n$ : | $33$ | |
| Transitive number $t$ : | $27$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,21,11,17,10,13,9,20,8,16,7,12,6,19,5,15,4,22,3,18,2,14)(23,30,26,33,29,25,32,28,24,31,27), (1,4,7,10,2,5,8,11,3,6,9)(12,30,17,28,22,26,16,24,21,33,15,31,20,29,14,27,19,25,13,23,18,32) | |
| $|\Aut(F/K)|$: | $11$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 6: $S_3$ 11: $C_{11}$ 22: 22T1 66: 33T2 726: 33T13 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 11: None
Low degree siblings
33T27 x 9Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 418 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $7986=2 \cdot 3 \cdot 11^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |