Group action invariants
| Degree $n$ : | $40$ | |
| Transitive number $t$ : | $15$ | |
| Group : | $C_5\times OD_{16}$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $2$ | |
| Generators: | (1,21,3,23,2,22,4,24)(5,26,7,28,6,25,8,27)(9,32,11,30,10,31,12,29)(13,35,16,34,14,36,15,33)(17,37,19,40,18,38,20,39), (1,14,25,37,10,24,33,6,18,30,3,15,27,40,12,21,35,8,20,31,2,13,26,38,9,23,34,5,17,29,4,16,28,39,11,22,36,7,19,32) | |
| $|\Aut(F/K)|$: | $20$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_4$ x 2, $C_2^2$ 5: $C_5$ 8: $C_4\times C_2$ 10: $C_{10}$ x 3 16: $C_8:C_2$ Resolvents shown for degrees $\leq 10$
Subfields
Degree 2: $C_2$
Degree 4: $C_4$
Degree 5: $C_5$
Degree 8: $C_8:C_2$
Degree 10: $C_{10}$
Degree 20: 20T1
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 50 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $80=2^{4} \cdot 5$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [80, 24] |
| Character table: Data not available. |