Group action invariants
| Degree $n$: | $33$ | |
| Transitive number $t$: | $41$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,18,25,6,19,23,4,12,26,7,17,27,8,15,31)(2,16,29,10,22,28,9,13,24,5,21,30,11,20,32)(3,14,33), (1,5,2,7,6,4,11,3,9,10)(12,17,16,14,21,13,19,20,22,15)(23,24,26,30,27,32,31,29,25,28) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $3$: $C_3$ $5$: $C_5$ $6$: $C_6$ $10$: $C_{10}$ $15$: $C_{15}$ $30$: $C_{30}$ $110$: $F_{11}$ $330$: 33T8 $3630$: 33T19 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 11: None
Low degree siblings
33T41 x 39Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 77 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. |