Properties

Label 46T20
Degree $46$
Order $94208$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 23: $C_{23}$

Low degree siblings

46T20 x 88

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 224 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $94208=2^{12} \cdot 23$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.