Group action invariants
| Degree $n$: | $40$ | |
| Transitive number $t$: | $16$ | |
| Group: | $C_5\times C_2^2:C_4$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $2$ | |
| $|\Aut(F/K)|$: | $20$ | |
| Generators: | (1,29,19,6,35,24,12,38,28,13,4,32,18,7,33,21,9,40,26,16)(2,30,20,5,36,23,11,37,27,14,3,31,17,8,34,22,10,39,25,15), (1,20,35,11,28,3,18,34,9,25)(2,19,36,12,27,4,17,33,10,26)(5,23,37,14,31,8,22,39,15,30)(6,24,38,13,32,7,21,40,16,29) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_4$ x 2, $C_2^2$ $5$: $C_5$ $8$: $D_{4}$ x 2, $C_4\times C_2$ $10$: $C_{10}$ x 3 $16$: $C_2^2:C_4$ Resolvents shown for degrees $\leq 10$
Subfields
Degree 2: $C_2$
Degree 5: $C_5$
Degree 8: $C_2^2:C_4$
Degree 10: $C_{10}$
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, 21] |
| Character table: not available. |