Properties

Label 46T42
Degree $46$
Order $2.081\times 10^{14}$
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)
$|\Aut(F/K)|$:  $1$
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)

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:  not available
Character table: not available.