Properties

Label 34T12
Order \(1156\)
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 $t$ :  $12$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,31,15,22)(2,34,14,19)(3,20,13,33)(4,23,12,30)(5,26,11,27)(6,29,10,24)(7,32,9,21)(8,18)(16,25,17,28), (1,22,14,27)(2,25,13,24)(3,28,12,21)(4,31,11,18)(5,34,10,32)(6,20,9,29)(7,23,8,26)(15,30,17,19)(16,33)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
4:  $C_4$
68:  $C_{17}:C_{4}$ x 2

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 17: None

Low degree siblings

34T12 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 76 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, 11]
Character table: Data not available.