Group action invariants
| Degree $n$ : | $46$ | |
| Transitive number $t$ : | $37$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,17,19,25,43,6,30,10,42,45,11,2,18,20,26,44,5,29,9,41,46,12)(3,24,37,33,21,31,16,13,7,35,27)(4,23,38,34,22,32,15,14,8,36,28), (1,10,2,9)(3,7,4,8)(5,6)(11,46)(12,45)(13,43)(14,44)(15,41)(16,42)(17,40)(18,39)(19,37)(20,38)(21,36,22,35)(23,34,24,33)(25,32,26,31)(27,29,28,30) | |
| $|\Aut(F/K)|$: | $2$ |
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: $F_{23}$ 1012: 46T6 2122317824: 46T35 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $F_{23}$
Low degree siblings
46T37Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 17,248 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $4244635648=2^{24} \cdot 11 \cdot 23$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |