Properties

Label 40T90338
Order \(163840\)
n \(40\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

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Group action invariants

Degree $n$:  $40$
Transitive number $t$:  $90338$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,5,2,6)(3,7,4,8)(9,11)(10,12)(13,15)(14,16)(17,18)(19,20)(27,28)(31,32)(33,34)(35,36)(37,38)(39,40), (1,9,28,23,33,3,11,25,22,35)(2,10,27,24,34,4,12,26,21,36)(5,13,30,20,39,7,15,32,18,38)(6,14,29,19,40,8,16,31,17,37), (1,18,9,38,31)(2,17,10,37,32)(3,19,11,40,30)(4,20,12,39,29)(5,21,13,35,25)(6,22,14,36,26)(7,23,15,34,27)(8,24,16,33,28)
$|\Aut(F/K)|$:  $2$

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: $C_2 \times (C_2^4 : C_5)$ x 3

Degree 20: 20T341

Low degree siblings

There are no siblings with degree $\leq 10$
Data on whether or not a number field with this Galois group has arithmetically equivalent fields has not been computed.

Conjugacy classes

There are 310 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $163840=2^{15} \cdot 5$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.