Properties

Label 46T42
Order \(208119169843200\)
n \(46\)
Cyclic No
Abelian No
Solvable No
Primitive No
$p$-group No

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$

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 170 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $208119169843200=2^{15} \cdot 3^{4} \cdot 5^{2} \cdot 7^{2} \cdot 11^{2} \cdot 23^{2}$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.