Properties

Label 16T1944
Order \(5160960\)
n \(16\)
Cyclic No
Abelian No
Solvable No
Primitive No
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $16$
Transitive number $t$ :  $1944$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,2)(3,5,14,12)(4,6,13,11)(7,16,8,15), (1,8,16,9,11,13,3,2,7,15,10,12,14,4)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
20160:  $A_8$
40320:  16T1839
2580480:  56T?

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: None

Degree 8: $A_8$

Low degree siblings

16T1944, 32T2711884

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 106 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $5160960=2^{14} \cdot 3^{2} \cdot 5 \cdot 7$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.