Properties

Label 34T10
Degree $34$
Order $578$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 17: None

Low degree siblings

34T10 x 7

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 170 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $578=2 \cdot 17^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  [578, 3]
Character table: not available.