# Properties

 Label 40T20 Order $$80$$ n $$40$$ Cyclic No Abelian No Solvable Yes Primitive No $p$-group No Group: $C_{10}\times D_4$

## Group action invariants

 Degree $n$ : $40$ Transitive number $t$ : $20$ Group : $C_{10}\times D_4$ Parity: $1$ Primitive: No Nilpotency class: $2$ Generators: (1,34,27,20,10,3,36,26,18,11,2,33,28,19,9,4,35,25,17,12)(5,39,32,24,15,7,38,29,21,13,6,40,31,23,16,8,37,30,22,14), (1,21)(2,22)(3,24)(4,23)(5,28)(6,27)(7,26)(8,25)(9,32)(10,31)(11,29)(12,30)(13,33)(14,34)(15,35)(16,36)(17,38)(18,37)(19,40)(20,39), (1,35,28,18,10)(2,36,27,17,9)(3,33,25,20,11,4,34,26,19,12)(5,37,31,21,15)(6,38,32,22,16)(7,40,30,24,13,8,39,29,23,14) $|\Aut(F/K)|$: $20$

## 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:  $D_{4}$ x 2, $C_2^3$
10:  $C_{10}$ x 7
16:  $D_4\times C_2$

Resolvents shown for degrees $\leq 10$

## Subfields

Degree 2: $C_2$ x 3

Degree 4: $C_2^2$, $D_{4}$ x 2

Degree 5: $C_5$

Degree 8: $D_4\times C_2$

Degree 10: $C_{10}$ x 3

Degree 20: 20T3, 20T12 x 2

## 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, 46]
 Character table: Data not available.