Group action invariants
| Degree $n$: | $33$ | |
| Transitive number $t$: | $42$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,29,16,11,28,22,8,25,18,10,27,17,5,33,14)(2,30,21,3,31,15,6,23,19,4,32,20,9,26,12)(7,24,13), (1,30,9,27,8,26,4,33,10,28)(2,31)(3,32,6,24,7,25,11,29,5,23)(12,22,13,20,17)(14,18,21,15,16) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $5$: $C_5$ $6$: $S_3$ $10$: $C_{10}$ $30$: $S_3 \times C_5$ $55$: $C_{11}:C_5$ $110$: 22T5 $330$: 33T7 $3630$: 33T20 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 11: None
Low degree siblings
33T42 x 9Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 98 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. |