Group action invariants
| Degree $n$: | $44$ | |
| Transitive number $t$: | $17$ | |
| Group: | $C_{11}\times S_4$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $11$ | |
| Generators: | (1,41,37,33,32,27,24,18,14,9,6,3,44,38,35,29,28,22,19,13,11,7,4,42,39,36,31,25,21,17,16,12,5)(2,43,40,34,30,26,23,20,15,10,8), (1,26,5,32,9,34,14,38,19,43,22,4,25,8,31,12,33,15,37,18,44,23,3,28,7,30,11,36,16,40,17,41,24,2,27,6,29,10,35,13,39,20,42,21) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $6$: $S_3$ $11$: $C_{11}$ $22$: 22T1 $24$: $S_4$ Resolvents shown for degrees $\leq 29$
Subfields
Degree 2: None
Degree 4: $S_4$
Degree 11: $C_{11}$
Degree 22: None
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 55 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $264=2^{3} \cdot 3 \cdot 11$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | [264, 31] |
| Character table: not available. |