Group action invariants
| Degree $n$ : | $44$ | |
| Transitive number $t$ : | $38$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,3)(2,4)(5,21)(6,22)(7,20)(8,19)(9,18)(10,17)(11,15)(12,16)(23,29)(24,30)(25,28)(26,27)(31,43)(32,44)(33,41)(34,42)(35,39)(36,40)(37,38), (1,34,21,24,19,35,17,26,15,38,14,28,11,40,10,29,8,41,5,31,3,43,2,33,22,23,20,36,18,25,16,37,13,27,12,39,9,30,7,42,6,32,4,44) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 8: $D_{4}$ 22: $D_{11}$ x 2 44: $D_{22}$ x 2 484: 22T9 Resolvents shown for degrees $\leq 29$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 11: None
Degree 22: 22T9
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 95 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, 20] |
| Character table: Data not available. |