Group action invariants
| Degree $n$: | $33$ | |
| Transitive number $t$: | $23$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $11$ | |
| Generators: | (1,18,31,2,22,25,3,15,30,4,19,24,5,12,29,6,16,23,7,20,28,8,13,33,9,17,27,10,21,32,11,14,26), (1,4,7,10,2,5,8,11,3,6,9)(12,20,17,14,22,19,16,13,21,18,15)(23,32,30,28,26,24,33,31,29,27,25) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $3$: $C_3$ $11$: $C_{11}$ $33$: $C_{33}$ $363$: 33T10 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 11: None
Low degree siblings
33T23 x 39Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 473 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $3993=3 \cdot 11^{3}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |