Properties

Label 20T964
Degree $20$
Order $983040$
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 $t$:  $964$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,9,4,12,20,14,2,10,3,11,19,13)(5,17,16,8,6,18,15,7), (3,15,13,6,4,16,14,5)(7,19,18,10)(8,20,17,9)(11,12)

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

20T964 x 3, 40T147546 x 2, 40T147716 x 2, 40T147838 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 155 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:  not available
Character table: not available.