Properties

Label 46T23
Degree $46$
Order $256036$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$11$:  $C_{11}$
$22$:  $D_{11}$, 22T1 x 3
$44$:  $D_{22}$, 44T2
$242$:  22T7
$484$:  44T27

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: None

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 169 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $256036=2^{2} \cdot 11^{2} \cdot 23^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.