Group action invariants
| Degree $n$: | $44$ | |
| Transitive number $t$: | $36$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $2$ | |
| Generators: | (1,26,12,41,21,35,9,29,19,24,7,40,17,34,6,28,15,44,4,37,14,32,2,25,11,42,22,36,10,30,20,23,8,39,18,33,5,27,16,43,3,38,13,31), (1,14)(2,13)(3,11)(4,12)(5,10)(6,9)(15,21)(16,22)(17,19)(18,20)(23,25)(24,26)(27,44)(28,43)(29,41)(30,42)(31,40)(32,39)(33,37)(34,38) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_4$ x 2, $C_2^2$ $8$: $C_4\times C_2$ $22$: $D_{11}$ x 2 $44$: $D_{22}$ x 2 $484$: 22T9 Resolvents shown for degrees $\leq 29$
Subfields
Degree 2: $C_2$
Degree 4: $C_4$
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 98 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $968=2^{3} \cdot 11^{2}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | [968, 18] |
| Character table: not available. |