Properties

Label 20T968
Order \(983040\)
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 $t$ :  $968$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,9,6,4,8)(2,10,5,3,7)(11,19,15,13,18,12,20,16,14,17), (1,5,14,2,6,13)(3,11,15,4,12,16)(7,8)(9,10)(19,20)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
60:  $A_5$
120:  $A_5\times C_2$
960:  $C_2^4 : A_5$ x 3
1920:  $C_2 \wr A_5$ x 3
15360:  20T468
30720:  20T561, 32T1123291 x 2

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: None

Degree 5: $A_5$

Degree 10: $C_2^4 : A_5$

Low degree siblings

20T963 x 2, 20T968, 40T147583, 40T147587, 40T147677, 40T147781, 40T147783 x 2

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 188 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.