Properties

Label 34T15
Order \(2312\)
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 $t$ :  $15$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,24,3,18,5,29,7,23,9,34,11,28,13,22,15,33,17,27,2,21,4,32,6,26,8,20,10,31,12,25,14,19,16,30), (1,26,16,20)(2,29,15,34)(3,32,14,31)(4,18,13,28)(5,21,12,25)(6,24,11,22)(7,27,10,19)(8,30,9,33)(17,23)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 17: None

Low degree siblings

34T13, 34T15

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 65 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $2312=2^{3} \cdot 17^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.