Properties

Label 46T15
Order \(23276\)
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 $t$ :  $15$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,30,16,26,15,37,12,24,3,31,22,29,10,46,20,28,4,43,2,42,19,39)(5,32)(6,44,8,45,14,25,9,34,17,38,18,27,21,40,7,33,11,35,23,41,13,36), (1,31,15,33,2,41,19,27,18,40,14,46,21,24,3,28,23,44,11,39,9,42)(4,38)(5,25,8,32,20,37,22,34,7,45,16,43,6,35,12,26,13,36,17,30,10,29)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
11:  $C_{11}$
22:  22T1 x 3
44:  44T2
506:  $F_{23}$ x 2
1012:  46T6 x 2

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: None

Low degree siblings

46T15 x 10

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 59 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $23276=2^{2} \cdot 11 \cdot 23^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.