Label 46T8
Degree $46$
Order $2116$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$46$:  $D_{23}$ x 2
$92$:  $D_{46}$ x 2

Resolvents shown for degrees $\leq 47$


Degree 2: $C_2$

Degree 23: None

Low degree siblings

46T8 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 169 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $2116=2^{2} \cdot 23^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.