Properties

Label 40T43472
Order \(81920\)
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 $t$ :  $43472$
Parity:  $1$
Primitive:  No
Generators:  (1,31,36,24,13,8,27,37,18,12,2,32,35,23,14,7,28,38,17,11)(3,29,33,21,15,6,25,40,20,10,4,30,34,22,16,5,26,39,19,9), (1,5,2,6)(3,8,4,7)(9,10)(15,16)(17,24,18,23)(19,21,20,22)(27,28)(31,32)(33,38,34,37)(35,39,36,40), (1,26,39,22,14,2,25,40,21,13)(3,27,38,23,15,4,28,37,24,16)(5,32,35,17,9,6,31,36,18,10)(7,29,34,19,12,8,30,33,20,11)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

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

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 176 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $81920=2^{14} \cdot 5$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.