Properties

Label 34T29
Degree $34$
Order $8704$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$17$:  $C_{17}$
$34$:  $C_{34}$
$4352$:  34T18

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 17: $C_{17}$

Low degree siblings

34T29 x 14

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 64 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $8704=2^{9} \cdot 17$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.