Group action invariants
| Degree $n$: | $40$ | |
| Transitive number $t$: | $19$ | |
| Group: | $C_5\times D_4:C_2$ | |
| Parity: | $1$ | |
| Primitive: | no | |
| Nilpotency class: | $2$ | |
| $|\Aut(F/K)|$: | $20$ | |
| Generators: | (3,4)(7,8)(11,12)(13,14)(19,20)(23,24)(25,26)(29,30)(33,34)(39,40), (1,30,18,7,35,23,10,39,28,13)(2,29,17,8,36,24,9,40,27,14)(3,31,19,5,34,21,11,37,25,15)(4,32,20,6,33,22,12,38,26,16), (1,34,28,19,10,3,35,25,18,11)(2,33,27,20,9,4,36,26,17,12)(5,40,31,24,15,8,37,29,21,14)(6,39,32,23,16,7,38,30,22,13) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 7 $4$: $C_2^2$ x 7 $5$: $C_5$ $8$: $C_2^3$ $10$: $C_{10}$ x 7 $16$: $Q_8:C_2$ Resolvents shown for degrees $\leq 10$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
Degree 5: $C_5$
Degree 8: $Q_8:C_2$
Degree 10: $C_{10}$ x 3
Degree 20: 20T3
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, 48] |
| Character table: not available. |