Properties

Label 20T1105
Order \(1857945600\)
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 $t$ :  $1105$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,10,14,12,19,5,3,17)(2,9,13,11,20,6,4,18), (1,2)(3,9,15)(4,10,16)(5,20,7,14)(6,19,8,13)(11,18,12,17)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
3628800:  $S_{10}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: None

Degree 5: None

Degree 10: $S_{10}$

Low degree siblings

20T1105, 40T252685

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 251 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $1857945600=2^{17} \cdot 3^{4} \cdot 5^{2} \cdot 7$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.