Properties

Label 46T23
Order \(256036\)
n \(46\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Learn more about

Group action invariants

Degree $n$ :  $46$
Transitive number $t$ :  $23$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
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)
$|\Aut(F/K)|$:  $1$

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:  Data not available
Character table: Data not available.