Group action invariants
| Degree $n$: | $44$ | |
| Transitive number $t$: | $27$ | |
| Group: | $C_{22}\times D_{11}$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $22$ | |
| Generators: | (1,29,3,43,6,35,8,28,10,42,11,33,13,26,16,40,17,31,20,23,22,37)(2,30,4,44,5,36,7,27,9,41,12,34,14,25,15,39,18,32,19,24,21,38), (1,30,13,25,3,44,16,39,6,36,17,32,8,27,20,24,10,41,22,38,11,34)(2,29,14,26,4,43,15,40,5,35,18,31,7,28,19,23,9,42,21,37,12,33) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $11$: $C_{11}$ $22$: $D_{11}$, 22T1 x 3 $44$: $D_{22}$ $242$: 22T7 Resolvents shown for degrees $\leq 29$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
Degree 11: None
Degree 22: 22T7
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 154 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $484=2^{2} \cdot 11^{2}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | [484, 10] |
| Character table: not available. |