Properties

Label 46T32
Degree $46$
Order $385875968$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$46$:  $D_{23}$
$92$:  $D_{46}$
$192937984$:  46T30

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 23: $D_{23}$

Low degree siblings

46T32 x 4093

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 188,528 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $385875968=2^{24} \cdot 23$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.