Properties

Label 46T33
Order \(1061158912\)
n \(46\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Learn more about

Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
11:  $C_{11}$
253:  $C_{23}:C_{11}$
518144:  46T25 x 2

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 16,624 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $1061158912=2^{22} \cdot 11 \cdot 23$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.