Group action invariants
| Degree $n$ : | $40$ | |
| Transitive number $t$ : | $105788$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,6,20,23,34,38,12,15,28,31)(2,5,19,24,33,37,11,16,27,32)(3,7,18,22,36,40,9,14,25,30,4,8,17,21,35,39,10,13,26,29), (1,29)(2,30)(3,32,4,31)(5,25,15,17,6,26,16,18)(7,28,13,19,8,27,14,20)(9,37,35,23)(10,38,36,24)(11,39,34,22)(12,40,33,21) | |
| $|\Aut(F/K)|$: | $2$ |
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: $C_2^2:C_4$ 32: $C_2^3 : C_4 $ 200: $D_5^2 : C_2$ Resolvents shown for degrees $\leq 10$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
Degree 5: None
Degree 8: None
Degree 10: $D_5^2 : C_2$
Degree 20: 20T50
Low degree siblings
There are no siblings with degree $\leq 10$
Data on whether or not a number field with this Galois group has arithmetically equivalent fields has not been computed.
Conjugacy Classes
There are 164 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $204800=2^{13} \cdot 5^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |