Properties

Label 46T32
Order \(385875968\)
n \(46\)
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)
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)
$|\Aut(F/K)|$:  $2$

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:  Data not available
Character table: Data not available.