Group action invariants
| Degree $n$: | $33$ | |
| Transitive number $t$: | $33$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,4,7,12,15,17,20,22,27,30,33)(2,6,8,11,13,16,21,24,25,29,31,3,5,9,10,14,18,19,23,26,28,32), (1,33,28,26,22,21,16,13,11,9,5,2,31,29,27,23,19,17,14,12,7,6,3,32,30,25,24,20,18,15,10,8,4) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $6$: $S_3$ $11$: $C_{11}$ $22$: 22T1 $66$: 33T2 $5346$: 33T24 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 11: $C_{11}$
Low degree siblings
33T33 x 21Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 66 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $16038=2 \cdot 3^{6} \cdot 11$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |