Properties

Label 46T35
Order \(2122317824\)
n \(46\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
11:  $C_{11}$
22:  22T1
506:  $F_{23}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 23: $F_{23}$

Low degree siblings

46T36

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

There are 8,624 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $2122317824=2^{23} \cdot 11 \cdot 23$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.