Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $654$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,15,9,4)(2,16,10,3)(5,7,6,8)(11,13,12,14)(17,20,18,19), (1,13,10,17)(2,14,9,18)(3,8,15,20,12)(4,7,16,19,11) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_4$ x 2, $C_2^2$ 8: $D_{4}$ x 2, $C_4\times C_2$ 16: $C_2^2:C_4$ 28800: $S_5^2 \wr C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $C_4$
Degree 5: None
Degree 10: $S_5^2 \wr C_2$
Low degree siblings
20T654, 20T657 x 2, 24T16045 x 2, 24T16046 x 2, 40T18813 x 2, 40T18816 x 2, 40T18818 x 2, 40T18819 x 2, 40T18821 x 2, 40T18829 x 2, 40T18841, 40T18842Siblings 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: | Data not available |
| Character table: Data not available. |