Group action invariants
| Degree $n$ : | $44$ | |
| Transitive number $t$ : | $49$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,24,7,31,14,39,20,25,3,34,9,41,15,27,22,36,5,44,12,29,17,38,2,23,8,32,13,40,19,26,4,33,10,42,16,28,21,35,6,43,11,30,18,37), (1,36,3,23,5,33,8,43,10,31,11,41,14,29,15,40,17,28,19,37,21,25)(2,35,4,24,6,34,7,44,9,32,12,42,13,30,16,39,18,27,20,38,22,26), (1,26,6,28,10,30,13,31,17,34,22,36,3,38,7,40,11,42,16,43,19,24,2,25,5,27,9,29,14,32,18,33,21,35,4,37,8,39,12,41,15,44,20,23) | |
| $|\Aut(F/K)|$: | $2$ |
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: $D_4\times C_2$ 22: $D_{11}$ x 2 44: $D_{22}$ x 6 484: 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 160 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, 134] |
| Character table: Data not available. |