Properties

Label 16T1945
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 $t$ :  $1945$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,16,2,15)(3,8,9,13,6)(4,7,10,14,5)(11,12), (1,10,8,15,13)(2,9,7,16,14)(3,11,5)(4,12,6)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
40320:  $S_8$
2580480:  56T?

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: None

Degree 8: $S_8$

Low degree siblings

16T1945, 32T2711885

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 100 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.