Group action invariants
| Degree $n$ : | $44$ | |
| Transitive number $t$ : | $37$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,32,11,25,22,41,9,35,19,30,8,23,18,40,6,34,15,27,3,43,13,38)(2,31,12,26,21,42,10,36,20,29,7,24,17,39,5,33,16,28,4,44,14,37), (1,10,18,4,11,20,6,14,22,7,15,2,9,17,3,12,19,5,13,21,8,16)(23,28,32,36,40,44,25,29,34,37,41,24,27,31,35,39,43,26,30,33,38,42), (1,41,6,40,9,38,13,35,18,34,22,32,3,30,8,27,11,25,15,23,19,43)(2,42,5,39,10,37,14,36,17,33,21,31,4,29,7,28,12,26,16,24,20,44) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 8: $C_2^3$ 22: $D_{11}$ x 2 44: $D_{22}$ x 6 484: 22T9 Resolvents shown for degrees $\leq 29$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
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 98 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, 39] |
| Character table: Data not available. |