Group action invariants
| Degree $n$: | $33$ | |
| Transitive number $t$: | $37$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,24,18,2,29,14,3,23,21,4,28,17,5,33,13,6,27,20,7,32,16,8,26,12,9,31,19,10,25,15,11,30,22), (1,23,16,2,28,12)(3,33,19,11,29,20)(4,27,15,10,24,13)(5,32,22,9,30,17)(6,26,18,8,25,21)(7,31,14) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $3$: $C_3$ $6$: $C_6$ $12$: $A_4$ $24$: $A_4\times C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 11: None
Low degree siblings
44T229Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 133 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $31944=2^{3} \cdot 3 \cdot 11^{3}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |