Group action invariants
| Degree $n$ : | $33$ | |
| Transitive number $t$ : | $28$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,17,6,19,11,21,5,12,10,14,4,16,9,18,3,20,8,22,2,13,7,15)(23,24)(25,33)(26,32)(27,31)(28,30), (1,28,21,8,30,16,4,32,22,11,23,17,7,25,12,3,27,18,10,29,13,6,31,19,2,33,14,9,24,20,5,26,15) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 6: $S_3$ 22: $D_{11}$ 66: $D_{33}$ 726: 33T13 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 11: None
Low degree siblings
33T28 x 9Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 253 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. |