Properties

Label 34T11
Degree $34$
Order $1156$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 17: None

Low degree siblings

34T11 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 100 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $1156=2^{2} \cdot 17^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  [1156, 13]
Character table: not available.