Properties

Label 40T73416
Degree $40$
Order $163840$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

Downloads

Learn more

Group action invariants

Degree $n$:  $40$
Transitive number $t$:  $73416$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$\card{\Aut(F/K)}$:  $2$
Generators:  (1,38,11,26,21)(2,37,12,25,22)(3,40,10,27,24,4,39,9,28,23)(5,34,15,32,18,6,33,16,31,17)(7,36,14,29,20)(8,35,13,30,19), (1,23,32,14,37,8,18,28,12,36)(2,24,31,13,38,7,17,27,11,35)(3,22,30,15,39,5,19,25,10,33)(4,21,29,16,40,6,20,26,9,34), (1,8,2,7)(3,6,4,5)(9,10)(11,12)(17,22,18,21)(19,23,20,24)(25,28)(26,27)(29,32)(30,31)(33,39,34,40)(35,37,36,38)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$5$:  $C_5$
$10$:  $C_{10}$ x 3
$80$:  $C_2^4 : C_5$ x 17
$160$:  $C_2 \times (C_2^4 : C_5)$ x 51

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 319 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $163840=2^{15} \cdot 5$
Cyclic:  no
Abelian:  no
Solvable:  yes
Label:  not available
Character table: not available.