Group action invariants
| Degree $n$ : | $40$ | |
| Transitive number $t$ : | $523$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,6,20,16)(2,5,19,15)(3,8,18,13)(4,7,17,14)(9,12,10,11)(21,32,35,28)(22,31,36,27)(23,30,33,26)(24,29,34,25)(37,40,38,39), (1,28,8,38)(2,27,7,37)(3,25,5,40)(4,26,6,39)(9,32,19,33)(10,31,20,34)(11,30,18,36)(12,29,17,35)(13,24,14,23)(15,22,16,21), (1,21,3,23,2,22,4,24)(5,37,7,40,6,38,8,39)(9,35,12,33,10,36,11,34)(13,29,15,32,14,30,16,31)(17,27,20,25,18,28,19,26), (1,4,2,3)(5,14,17,10)(6,13,18,9)(7,16,20,11)(8,15,19,12)(21,27,39,33)(22,28,40,34)(23,25,37,36)(24,26,38,35)(29,32,30,31) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 15 4: $C_4$ x 8, $C_2^2$ x 35 8: $D_{4}$ x 4, $C_4\times C_2$ x 28, $C_2^3$ x 15 16: $D_4\times C_2$ x 6, $Q_8:C_2$ x 2 20: $F_5$ 32: $Z_8 : Z_8^\times$ x 2 40: $F_{5}\times C_2$ x 7 Resolvents shown for degrees $\leq 10$
Subfields
Degree 2: $C_2$
Degree 4: $D_{4}$
Degree 5: $F_5$
Degree 8: $Z_8 : Z_8^\times$
Degree 10: $F_{5}\times C_2$
Degree 20: 20T42
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 55 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $640=2^{7} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [640, 19528] |
| Character table: Data not available. |