Group action invariants
| Degree $n$ : | $20$ | |
| Transitive number $t$ : | $781$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,13,2,14)(3,11,4,12)(5,19,6,20)(7,17,10,16)(8,18,9,15), (1,18,3,12,7,20,5,14)(2,17,4,11,8,19,6,13)(9,16)(10,15), (1,16,7,12)(2,15,8,11)(3,20)(4,19)(5,18,9,14)(6,17,10,13) | |
| $|\Aut(F/K)|$: | $2$ |
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 6, $C_2^3$ 16: $D_4\times C_2$ x 3 32: $C_2^2 \wr C_2$ 28800: $S_5^2 \wr C_2$ 57600: 20T655 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 5: None
Degree 10: $S_5^2 \wr C_2$
Low degree siblings
20T781 x 7, 24T17918 x 8, 40T45487 x 4, 40T45488 x 8, 40T45489 x 8, 40T45497 x 4, 40T45508 x 4, 40T45542 x 8, 40T45559 x 4, 40T45560 x 4Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 119 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $115200=2^{9} \cdot 3^{2} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |