Group action invariants
| Degree $n$: | $20$ | |
| Transitive number $t$: | $656$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $2$ | |
| Generators: | (1,15,9,4,13,20,5,7,17,12)(2,16,10,3,14,19,6,8,18,11), (1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20), (1,11)(2,12)(3,13,16,9,8,17,19,5)(4,14,15,10,7,18,20,6) |
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, $C_2^3$ $16$: $D_4\times C_2$ $28800$: $S_5^2 \wr C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
Degree 5: None
Degree 10: $S_5^2 \wr C_2$
Low degree siblings
20T655 x 2, 20T656, 24T16043 x 2, 24T16044 x 2, 40T18814 x 2, 40T18815 x 2, 40T18817 x 2, 40T18820 x 2, 40T18822 x 2, 40T18830 x 2, 40T18839, 40T18840Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 70 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: | not available |
| Character table: not available. |