Group action invariants
| Degree $n$: | $33$ | |
| Transitive number $t$: | $44$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $3$ | |
| Generators: | (1,4,18,33,26,2,5,16,31,27,3,6,17,32,25)(7,29,15,20,12,8,30,13,21,10,9,28,14,19,11)(22,24,23), (1,22,30,26,11,3,24,29,25,10,2,23,28,27,12)(7,20,14,16,31)(8,21,15,17,32)(9,19,13,18,33) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $3$: $C_3$ $5$: $C_5$ $15$: $C_{15}$ $55$: $C_{11}:C_5$ $165$: 33T6 $13365$: 33T30 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 11: $C_{11}:C_5$
Low degree siblings
33T44Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 63 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $40095=3^{6} \cdot 5 \cdot 11$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |