Properties

Label 46T16
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 $t$ :  $16$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,12,13,11,15,7,23,14,9,19,22,16,5,4,6,2,10,17,3,8,21,18)(24,32,39,25,30,43,40,46,34,35,33,37,29,45,36,31,41,44,38,27,26,28), (1,41,17,43,14,34,16,40,7,36,13,31,9,42,4,27,15,37,23,38,10,45,11,25,18,46,21,32,19,26,5,30,22,35,3,24,8,39,20,29,12,28,2,44)(6,33)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
4:  $C_4$
11:  $C_{11}$
22:  22T1
44:  $C_{44}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: None

Low degree siblings

46T16 x 11

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