Group action invariants
| Degree $n$ : | $44$ | |
| Transitive number $t$ : | $48$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (3,22)(4,21)(5,19)(6,20)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)(23,30)(24,29)(25,28)(26,27)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38), (1,33,8,41)(2,34,7,42)(3,44,5,32)(4,43,6,31)(9,30,22,24)(10,29,21,23)(11,39,19,35)(12,40,20,36)(13,28,17,26)(14,27,18,25)(15,38)(16,37) | |
| $|\Aut(F/K)|$: | $2$ |
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: $D_{4}$ x 2, $C_4\times C_2$ 16: $C_2^2:C_4$ 484: 22T8 Resolvents shown for degrees $\leq 29$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
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 130 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, 116] |
| Character table: Data not available. |