Group action invariants
| Degree $n$: | $40$ | |
| Transitive number $t$: | $73416$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $\card{\Aut(F/K)}$: | $2$ | |
| Generators: | (1,38,11,26,21)(2,37,12,25,22)(3,40,10,27,24,4,39,9,28,23)(5,34,15,32,18,6,33,16,31,17)(7,36,14,29,20)(8,35,13,30,19), (1,23,32,14,37,8,18,28,12,36)(2,24,31,13,38,7,17,27,11,35)(3,22,30,15,39,5,19,25,10,33)(4,21,29,16,40,6,20,26,9,34), (1,8,2,7)(3,6,4,5)(9,10)(11,12)(17,22,18,21)(19,23,20,24)(25,28)(26,27)(29,32)(30,31)(33,39,34,40)(35,37,36,38) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $5$: $C_5$ $10$: $C_{10}$ x 3 $80$: $C_2^4 : C_5$ x 17 $160$: $C_2 \times (C_2^4 : C_5)$ x 51 Resolvents shown for degrees $\leq 10$
Subfields
Degree 2: None
Degree 4: None
Degree 5: $C_5$
Degree 8: None
Degree 10: $C_2^4 : C_5$, $C_2 \times (C_2^4 : C_5)$ x 2
Degree 20: 20T263
Low degree siblings
There are no siblings with degree $\leq 10$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 319 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $163840=2^{15} \cdot 5$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| Label: | not available |
| Character table: not available. |