Group action invariants
| Degree $n$ : | $44$ | |
| Transitive number $t$ : | $33$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,33,11,37,22,42,10,23,20,28,8,31,17,35,6,40,16,43,3,26,13,29)(2,34,12,38,21,41,9,24,19,27,7,32,18,36,5,39,15,44,4,25,14,30), (1,25,2,26)(3,39,4,40)(5,31,6,32)(7,23,8,24)(9,37,10,38)(11,30,12,29)(13,44,14,43)(15,35,16,36)(17,27,18,28)(19,42,20,41)(21,33,22,34) | |
| $|\Aut(F/K)|$: | $22$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 8: $D_{4}$ 11: $C_{11}$ 22: $D_{11}$, 22T1 x 3 44: $D_{22}$ 242: 22T7 Resolvents shown for degrees $\leq 29$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 11: None
Degree 22: 22T7
Low degree siblings
There are no siblings with degree $\leq 29$
Data on whether or not a number field with this Galois group has arithmetically equivalent fields has not been computed.
Conjugacy Classes
There are 275 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $968=2^{3} \cdot 11^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [968, 26] |
| Character table: Data not available. |