Group action invariants
| Degree $n$ : | $44$ | |
| Transitive number $t$ : | $50$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,32,15,27,8,23,22,41,14,37,5,34,20,29,12,26,3,44,17,39,10,35)(2,31,16,28,7,24,21,42,13,38,6,33,19,30,11,25,4,43,18,40,9,36), (1,21)(2,22)(3,19)(4,20)(5,18)(6,17)(7,15)(8,16)(9,14)(10,13)(11,12)(23,25)(24,26)(27,43)(28,44)(29,42)(30,41)(31,39)(32,40)(33,37)(34,38)(35,36), (1,25,14,31)(2,26,13,32)(3,38,12,42)(4,37,11,41)(5,28,10,30)(6,27,9,29)(7,39)(8,40)(15,43,22,36)(16,44,21,35)(17,33,20,24)(18,34,19,23) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 8: $D_{4}$ x 2, $C_2^3$ 16: $D_4\times C_2$ 968: 22T10 Resolvents shown for degrees $\leq 29$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
Degree 11: None
Degree 22: 22T10
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 70 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1936=2^{4} \cdot 11^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [1936, 161] |
| Character table: Data not available. |