Properties

Label 46T22
Degree $46$
Order $256036$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

Learn more about

Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$4$:  $C_4$
$11$:  $C_{11}$
$22$:  $D_{11}$, 22T1
$44$:  $C_{44}$, 44T3
$242$:  22T7
$484$:  44T26

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 166 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.