Properties

Label 40T89829
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 $t$ :  $89829$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,33,21,30,11,2,34,22,29,12)(3,35,24,31,10,4,36,23,32,9)(5,39,18,27,16,6,40,17,28,15)(7,38,20,25,13,8,37,19,26,14), (1,30,35,9,22,3,32,33,11,24,2,29,36,10,21,4,31,34,12,23)(5,28,37,13,17,8,26,39,16,19,6,27,38,14,18,7,25,40,15,20), (1,40,24,32,14,7,35,17,27,12)(2,39,23,31,13,8,36,18,28,11)(3,38,21,29,15,6,33,20,26,10)(4,37,22,30,16,5,34,19,25,9)
$|\Aut(F/K)|$:  $2$

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 313 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.