Properties

Label 46T34
Degree $46$
Order $2122317824$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$11$:  $C_{11}$
$22$:  22T1
$253$:  $C_{23}:C_{11}$
$506$:  46T4
$518144$:  46T25 x 2
$1036288$:  46T26 x 2
$1061158912$:  46T33

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 23: $C_{23}:C_{11}$

Low degree siblings

There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

There are 33,248 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $2122317824=2^{23} \cdot 11 \cdot 23$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.