Group action invariants
| Degree $n$: | $46$ | |
| Transitive number $t$: | $24$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,9,8,11,2,6,17,7,14,16,10,5,20,21,18,4,23,12,22,15,13,19)(24,32,41,31,37,38,42,35,30,33,45)(25,36,34,26,40,27,44,43,39,46,28), (1,40,11,25,5,34,4,24,23,30,7,31,12,35,9,28,20,46,18,26,10,38)(2,27,15,42,21,33,22,43,3,37,19,36,14,32,17,39,6,44,8,41,16,29)(13,45) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $8$: $D_{4}$ $11$: $C_{11}$ $22$: $D_{11}$, 22T1 x 3 $44$: $D_{22}$, 44T2 $88$: 44T5, 44T6 $242$: 22T7 $484$: 44T27 $968$: 44T33 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 23: None
Low degree siblings
There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 299 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $512072=2^{3} \cdot 11^{2} \cdot 23^{2}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |