Properties

Label 46T29
Degree $46$
Order $192937984$
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)
$|\Aut(F/K)|$:  $2$
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)

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:  not available
Character table: not available.