Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $658$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,14,8,19)(2,13,7,20)(3,11,10,18)(4,12,9,17)(5,15)(6,16), (1,19,4,17,9,12,6,14,8,16)(2,20,3,18,10,11,5,13,7,15), (1,16,5,13,4,17,7,20,9,12,2,15,6,14,3,18,8,19,10,11) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_2^2$ x 7 8: $D_{4}$ x 2, $C_2^3$ 16: $D_4\times C_2$ 14400: $(A_5^2 : C_2):C_2$ 28800: 20T548 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 5: None
Degree 10: $(A_5^2 : C_2):C_2$
Low degree siblings
20T658 x 3, 24T16041 x 4, 40T18798 x 2, 40T18805 x 4, 40T18806 x 4, 40T18863 x 2, 40T18864 x 2Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 76 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $57600=2^{8} \cdot 3^{2} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |