Properties

Label 20T966
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 $t$ :  $966$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,6,9,4,7,2,5,10,3,8)(11,15,20,13,17,12,16,19,14,18), (1,5,19,4,12,16,10,14,2,6,20,3,11,15,9,13)(7,8)(17,18)
$|\Aut(F/K)|$:  $2$

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

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

20T966 x 3, 40T147542 x 2, 40T147713 x 2, 40T147718 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 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.