Properties

Label 46T39
Degree $46$
Order $41783132160$
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)
$|\Aut(F/K)|$:  $2$
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)

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:  not available
Character table: not available.