Group action invariants
| Degree $n$ : | $33$ | |
| Transitive number $t$ : | $32$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,31,9,27,6,23,3,30,11,26,8,33,5,29,2,25,10,32,7,28,4,24)(12,15,18,21,13,16,19,22,14,17,20), (1,2)(3,11)(4,10)(5,9)(6,8)(12,24,17,26,22,28,16,30,21,32,15,23,20,25,14,27,19,29,13,31,18,33) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 6: $S_3$ 12: $D_{6}$ 22: $D_{11}$ 44: $D_{22}$ 132: 33T5 1452: 33T15 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 11: None
Low degree siblings
33T32 x 9Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 221 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $15972=2^{2} \cdot 3 \cdot 11^{3}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |