Properties

Label 46T19
Order \(47104\)
n \(46\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

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Group action invariants

Degree $n$ :  $46$
Transitive number $t$ :  $19$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,11,21,31,41,5,16,25,35,45,9,19,29,39,4,14,24,34,43,8,18,27,38)(2,12,22,32,42,6,15,26,36,46,10,20,30,40,3,13,23,33,44,7,17,28,37), (1,34,20,5,37,23,10,42,27,14,45,31,18,3,35,21,7,39,25,11,43,29,16)(2,33,19,6,38,24,9,41,28,13,46,32,17,4,36,22,8,40,26,12,44,30,15)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
23:  $C_{23}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 23: $C_{23}$

Low degree siblings

46T19 x 88

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 112 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $47104=2^{11} \cdot 23$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.