Properties

Label 34T16
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 $t$ :  $16$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,31,9,24)(2,28,8,27)(3,25,7,30)(4,22,6,33)(5,19)(10,21,17,34)(11,18,16,20)(12,32,15,23)(13,29,14,26), (1,32,12,28,6,24,17,20,11,33,5,29,16,25,10,21,4,34,15,30,9,26,3,22,14,18,8,31,2,27,13,23,7,19)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_4$ x 2, $C_2^2$
8:  $C_4\times C_2$
68:  $C_{17}:C_{4}$ x 2
136:  34T5 x 2

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 17: None

Low degree siblings

34T16 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 56 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.