Properties

Label 20T1025
Order \(7372800\)
n \(20\)
Cyclic No
Abelian No
Solvable No
Primitive No
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $20$
Transitive number $t$ :  $1025$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,9,14,5,17,2,10,13,6,18)(3,19,16,11,7,4,20,15,12,8), (1,11,13,16,18,19,10,4)(2,12,14,15,17,20,9,3)(5,8)(6,7)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_4$ x 2, $C_2^2$
8:  $C_4\times C_2$
14400:  $A_5^2 : C_4$
28800:  20T541
3686400:  20T1011

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: None

Degree 5: None

Degree 10: $A_5^2 : C_4$

Low degree siblings

20T1027, 40T171498, 40T171513, 40T171514, 40T171515, 40T171516, 40T171527, 40T171528, 40T171535, 40T171536

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

There are 216 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $7372800=2^{15} \cdot 3^{2} \cdot 5^{2}$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.