Properties

Label 16T1916
Order \(344064\)
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 $t$ :  $1916$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,8,12,13,3,16,2,7,11,14,4,15)(5,10,6,9), (1,2)(3,16,7,5,10,11,13)(4,15,8,6,9,12,14)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
168:  $\GL(3,2)$
336:  14T17
1344:  $C_2^3:\GL(3,2)$
2688:  14T43
21504:  16T1801
172032:  56T?

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 4: None

Degree 8: $C_2^3:\GL(3,2)$

Low degree siblings

16T1916, 32T2267427

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 79 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $344064=2^{14} \cdot 3 \cdot 7$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.