Properties

Label 46T39
Order \(41783132160\)
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 $t$ :  $39$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,42)(2,41)(3,25,10,46,13,6,4,26,9,45,14,5)(7,22,15)(8,21,16)(11,12)(17,38,27)(18,37,28)(19,33,36,40,43,23)(20,34,35,39,44,24)(29,31,30,32), (1,45,42,26,30,44,34,39,3,5,35,21,12,13,24,10,38,28,8,19,16,31,18)(2,46,41,25,29,43,33,40,4,6,36,22,11,14,23,9,37,27,7,20,15,32,17)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
10200960:  $M_{23}$
20401920:  46T27
20891566080:  46T38

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 23: $M_{23}$

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 120 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $41783132160=2^{19} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 23$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.