Group action invariants
| Degree $n$: | $33$ | |
| Transitive number $t$: | $29$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $3$ | |
| Generators: | (1,33,29,26,23,20,17,13,11,8,5,2,31,30,27,24,21,18,14,12,9,6,3,32,28,25,22,19,16,15,10,7,4), (1,22,11,31,20,9,28,16,6,25,15,2,23,12,32,21,7,29,17,4,26,13,3,24,10,33,19,8,30,18,5,27,14) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $3$: $C_3$ $11$: $C_{11}$ $33$: $C_{33}$ $2673$: 33T18 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 11: $C_{11}$
Low degree siblings
33T29 x 21Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 99 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $8019=3^{6} \cdot 11$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | [8019, 505] |
| Character table: not available. |