# Properties

 Label 40T43472 Order $$81920$$ n $$40$$ Cyclic No Abelian No Solvable Yes Primitive No $p$-group No

## Group action invariants

 Degree $n$ : $40$ Transitive number $t$ : $43472$ Parity: $1$ Primitive: No Generators: (1,31,36,24,13,8,27,37,18,12,2,32,35,23,14,7,28,38,17,11)(3,29,33,21,15,6,25,40,20,10,4,30,34,22,16,5,26,39,19,9), (1,5,2,6)(3,8,4,7)(9,10)(15,16)(17,24,18,23)(19,21,20,22)(27,28)(31,32)(33,38,34,37)(35,39,36,40), (1,26,39,22,14,2,25,40,21,13)(3,27,38,23,15,4,28,37,24,16)(5,32,35,17,9,6,31,36,18,10)(7,29,34,19,12,8,30,33,20,11) $|\Aut(F/K)|$: $2$

## Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
5:  $C_5$
10:  $C_{10}$
80:  $C_2^4 : C_5$ x 17
160:  $C_2 \times (C_2^4 : C_5)$ x 17

Resolvents shown for degrees $\leq 10$

## Subfields

Degree 2: None

Degree 4: None

Degree 5: $C_5$

Degree 8: None

Degree 10: $C_2^4 : C_5$, $C_2 \times (C_2^4 : C_5)$ x 2

Degree 20: 20T263

## 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 176 conjugacy classes of elements. Data not shown.

## Group invariants

 Order: $81920=2^{14} \cdot 5$ Cyclic: No Abelian: No Solvable: Yes GAP id: Data not available
 Character table: Data not available.