Properties

Label 34T45
Order \(17408\)
n \(34\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

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Group action invariants

Degree $n$ :  $34$
Transitive number $t$ :  $45$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,21,8,28,13,34,19,5,25,12,32,18,3,24,10,29,16,2,22,7,27,14,33,20,6,26,11,31,17,4,23,9,30,15), (1,31)(2,32)(3,29)(4,30)(5,27,6,28)(7,25)(8,26)(9,23)(10,24)(11,22)(12,21)(13,20,14,19)(15,17,16,18)(33,34)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
34:  $D_{17}$
68:  $D_{34}$
8704:  34T30

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 17: $D_{17}$

Low degree siblings

34T45 x 29

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 80 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $17408=2^{10} \cdot 17$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.