Group action invariants
| Degree $n$ : | $44$ | |
| Transitive number $t$ : | $26$ | |
| Group : | $C_{11}\times C_{11}:C_4$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,3,5,7,9,12,14,15,18,19,21,2,4,6,8,10,11,13,16,17,20,22)(23,33,44,31,42,30,39,28,38,25,35,24,34,43,32,41,29,40,27,37,26,36), (1,38,6,43,9,27,13,33,18,39,22,24,4,29,7,36,11,42,15,25,20,32,2,37,5,44,10,28,14,34,17,40,21,23,3,30,8,35,12,41,16,26,19,31) | |
| $|\Aut(F/K)|$: | $22$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 4: $C_4$ 11: $C_{11}$ 22: $D_{11}$, 22T1 242: 22T7 Resolvents shown for degrees $\leq 29$
Subfields
Degree 2: $C_2$
Degree 4: $C_4$
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, 5] |
| Character table: Data not available. |