Group action invariants
| Degree $n$: | $46$ | |
| Transitive number $t$: | $22$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,45,15,28,21,24,17,42,12,30,23,38,8,25,18,26,19,33,3,36,6,34,4,43,13,37,7,41,11,46,16,35,5,27,20,40,10,39,9,32,2,29,22,31)(14,44), (1,36,7,44,12,43,20,46,19,37,22,41,13,29,17,42,5,26,18,28,2,45,4,40,21,32,16,33,8,30,9,39,6,35,15,24,11,34,23,27,10,25,3,31)(14,38) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $4$: $C_4$ $11$: $C_{11}$ $22$: $D_{11}$, 22T1 $44$: $C_{44}$, 44T3 $242$: 22T7 $484$: 44T26 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 166 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $256036=2^{2} \cdot 11^{2} \cdot 23^{2}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |