Properties

Label 40T19
Order \(80\)
n \(40\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $C_5\times D_4:C_2$

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Group action invariants

Degree $n$ :  $40$
Transitive number $t$ :  $19$
Group :  $C_5\times D_4:C_2$
Parity:  $1$
Primitive:  No
Nilpotency class:  $2$
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)
$|\Aut(F/K)|$:  $20$

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:  $C_2^3$
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: Data not available.