Properties

Label 46T26
Degree $46$
Order $1036288$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

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

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 64 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $1036288=2^{12} \cdot 11 \cdot 23$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.