Group action invariants
| Degree $n$: | $46$ | |
| Transitive number $t$: | $15$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,30,16,26,15,37,12,24,3,31,22,29,10,46,20,28,4,43,2,42,19,39)(5,32)(6,44,8,45,14,25,9,34,17,38,18,27,21,40,7,33,11,35,23,41,13,36), (1,31,15,33,2,41,19,27,18,40,14,46,21,24,3,28,23,44,11,39,9,42)(4,38)(5,25,8,32,20,37,22,34,7,45,16,43,6,35,12,26,13,36,17,30,10,29) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $11$: $C_{11}$ $22$: 22T1 x 3 $44$: 44T2 $506$: $F_{23}$ x 2 $1012$: 46T6 x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 23: None
Low degree siblings
46T15 x 10Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 59 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. |