Properties

Label 40T15
Order \(80\)
n \(40\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $C_5\times OD_{16}$

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Group action invariants

Degree $n$ :  $40$
Transitive number $t$ :  $15$
Group :  $C_5\times OD_{16}$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $2$
Generators:  (1,21,3,23,2,22,4,24)(5,26,7,28,6,25,8,27)(9,32,11,30,10,31,12,29)(13,35,16,34,14,36,15,33)(17,37,19,40,18,38,20,39), (1,14,25,37,10,24,33,6,18,30,3,15,27,40,12,21,35,8,20,31,2,13,26,38,9,23,34,5,17,29,4,16,28,39,11,22,36,7,19,32)
$|\Aut(F/K)|$:  $20$

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:  $C_4\times C_2$
10:  $C_{10}$ x 3
16:  $C_8:C_2$

Resolvents shown for degrees $\leq 10$

Subfields

Degree 2: $C_2$

Degree 4: $C_4$

Degree 5: $C_5$

Degree 8: $C_8:C_2$

Degree 10: $C_{10}$

Degree 20: 20T1

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, 24]
Character table: Data not available.