Group action invariants
| Degree $n$ : | $44$ | |
| Transitive number $t$ : | $35$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,29,3,42)(2,30,4,41)(5,32,22,39)(6,31,21,40)(7,44,20,28)(8,43,19,27)(9,34,18,37)(10,33,17,38)(11,24,16,25)(12,23,15,26)(13,36)(14,35), (1,37,17,30)(2,38,18,29)(3,25,15,41)(4,26,16,42)(5,36,14,31)(6,35,13,32)(7,23,11,43)(8,24,12,44)(9,33)(10,34)(19,39,21,28)(20,40,22,27) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_4$ x 2, $C_2^2$ 8: $C_4\times C_2$ 484: 22T8 Resolvents shown for degrees $\leq 29$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
Degree 11: None
Degree 22: 22T8
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 68 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, 38] |
| Character table: Data not available. |