Properties

Label 20T965
Order \(983040\)
n \(20\)
Cyclic No
Abelian No
Solvable No
Primitive No
$p$-group No

Related objects

Learn more about

Group action invariants

Degree $n$ :  $20$
Transitive number $t$ :  $965$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,17,15)(2,18,16)(3,20)(4,19)(5,11,8)(6,12,7)(9,13,10,14), (1,3,12,14)(2,4,11,13)(5,9,7,15,20,18,6,10,8,16,19,17)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
120:  $S_5$
1920:  $(C_2^4:A_5) : C_2$ x 3
30720:  20T555
61440:  32T1520177

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: None

Degree 5: $S_5$

Degree 10: $(C_2^4:A_5) : C_2$

Low degree siblings

20T962 x 2, 20T965, 40T147541, 40T147545, 40T147714, 40T147719 x 2, 40T147837

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 149 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $983040=2^{16} \cdot 3 \cdot 5$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.