Group action invariants
| Degree $n$: | $33$ | |
| Transitive number $t$: | $28$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| 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) |
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: | not available |
| Character table: not available. |