Label 46T16
Degree $46$
Order $23276$
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)
$|\Aut(F/K)|$:  $1$
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)

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 $\leq 47$


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:  not available
Character table: not available.