Properties

Label 34T11
Order \(1156\)
n \(34\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Learn more about

Group action invariants

Degree $n$ :  $34$
Transitive number $t$ :  $11$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
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)
$|\Aut(F/K)|$:  $1$

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: Data not available.