Group action invariants
| Degree $n$: | $44$ | |
| Transitive number $t$: | $5$ | |
| Group: | $C_{11}\times D_4$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $2$ | |
| $|\Aut(F/K)|$: | $22$ | |
| Generators: | (1,36,25,15,6,40,30,19,10,44,33,23,14,3,38,27,18,8,42,32,21,12,2,35,26,16,5,39,29,20,9,43,34,24,13,4,37,28,17,7,41,31,22,11), (1,44,41,40,37,36,34,31,29,28,26,24,21,20,18,16,14,12,10,8,6,3)(2,43,42,39,38,35,33,32,30,27,25,23,22,19,17,15,13,11,9,7,5,4) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $8$: $D_{4}$ $11$: $C_{11}$ $22$: 22T1 x 3 Resolvents shown for degrees $\leq 29$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 11: $C_{11}$
Degree 22: 22T1
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: | $88=2^{3} \cdot 11$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | [88, 9] |
| Character table: not available. |