# Properties

 Label 40T16 Order $$80$$ n $$40$$ Cyclic No Abelian No Solvable Yes Primitive No $p$-group No Group: $C_5\times C_2^2:C_4$

## 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: $2$ 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) $|\Aut(F/K)|$: $20$

## 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:  $D_{4}$ 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 4: $C_4$, $D_{4}$ x 2

Degree 5: $C_5$

Degree 8: $C_2^2:C_4$

Degree 10: $C_{10}$

Degree 20: 20T1, 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, 21]
 Character table: Data not available.