Properties

Label 20T1013
Order \(3686400\)
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 $t$ :  $1013$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,17,10,11,8,15,5,14,3,19)(2,18,9,12,7,16,6,13,4,20), (1,4,7,2,3,8)(5,10,6,9)(11,12)(13,17,19,15,14,18,20,16)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
14400:  $(A_5^2 : C_2):C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 4: None

Degree 5: None

Degree 10: $(A_5^2 : C_2):C_2$

Low degree siblings

20T1009, 32T2660825, 40T162001, 40T162004, 40T162005, 40T162006, 40T162007

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 114 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $3686400=2^{14} \cdot 3^{2} \cdot 5^{2}$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.