Group action invariants
| Degree $n$: | $46$ | |
| Transitive number $t$: | $16$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,12,13,11,15,7,23,14,9,19,22,16,5,4,6,2,10,17,3,8,21,18)(24,32,39,25,30,43,40,46,34,35,33,37,29,45,36,31,41,44,38,27,26,28), (1,41,17,43,14,34,16,40,7,36,13,31,9,42,4,27,15,37,23,38,10,45,11,25,18,46,21,32,19,26,5,30,22,35,3,24,8,39,20,29,12,28,2,44)(6,33) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $4$: $C_4$ $11$: $C_{11}$ $22$: 22T1 $44$: $C_{44}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 23: None
Low degree siblings
46T16 x 11Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 56 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $23276=2^{2} \cdot 11 \cdot 23^{2}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | not available |
| Character table: not available. |