Group action invariants
| Degree $n$: | $33$ | |
| Transitive number $t$: | $43$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,22,31)(2,14,29,4,20,25,10,16,24,6,15,32,5,12,23)(3,17,27,7,18,30,8,21,28,11,19,33,9,13,26), (1,15,7,18,4,22,11,20,2,21)(3,16,6,12,10,14,8,13,9,19)(5,17)(24,30,28,25,26,33,27,29,32,31) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $5$: $C_5$ $6$: $S_3$ $10$: $C_{10}$ $30$: $S_3 \times C_5$ $110$: $F_{11}$ $330$: 33T9 $3630$: 33T20 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 11: None
Low degree siblings
33T43 x 9Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 65 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $39930=2 \cdot 3 \cdot 5 \cdot 11^{3}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |