Group action invariants
| Degree $n$ : | $33$ | |
| Transitive number $t$ : | $26$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,18,32,10,15,33)(2,14,26,9,19,28)(3,21,31,8,12,23)(4,17,25,7,16,29)(5,13,30,6,20,24)(11,22,27), (1,15,31,2,19,25,3,12,30,4,16,24,5,20,29,6,13,23,7,17,28,8,21,33,9,14,27,10,18,32,11,22,26) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 3: $C_3$ 6: $C_6$ 22: $D_{11}$ 66: 33T4 726: 33T12 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 11: None
Low degree siblings
33T26 x 39Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 241 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. |