Group action invariants
| Degree $n$: | $46$ | |
| Transitive number $t$: | $38$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $2$ | |
| Generators: | (1,18,37)(2,17,38)(3,11,22,4,12,21)(5,7,14,6,8,13)(9,34,35)(10,33,36)(15,44,39)(16,43,40)(19,46,25)(20,45,26)(27,28)(29,30), (1,39,34,17,27,21,36,4,12,10,46,23,41,16,20,44,6,13,8,37,31,25,29)(2,40,33,18,28,22,35,3,11,9,45,24,42,15,19,43,5,14,7,38,32,26,30) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $10200960$: $M_{23}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 23: $M_{23}$
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 60 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $20891566080=2^{18} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 23$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | no | |
| GAP id: | not available |
| Character table: not available. |