Properties

Label 46T29
Order \(192937984\)
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 $t$ :  $29$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,46,43,42,39,38,36,34,32,29,27,26,24,21,19,18,15,14,12,9,7,5,4)(2,45,44,41,40,37,35,33,31,30,28,25,23,22,20,17,16,13,11,10,8,6,3), (1,20,37,9,27,45,18,36,7,26,44,16,33,5,23,41,13,31,4,21,39,12,29,2,19,38,10,28,46,17,35,8,25,43,15,34,6,24,42,14,32,3,22,40,11,30)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
23:  $C_{23}$
46:  $C_{46}$
47104:  46T19 x 2
94208:  46T20 x 2
96468992:  46T28

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 23: $C_{23}$

Low degree siblings

46T29 x 182182

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 364,768 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $192937984=2^{23} \cdot 23$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.