Properties

Label 46T18
Degree $46$
Order $46552$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$8$:  $D_{4}$
$11$:  $C_{11}$
$22$:  22T1 x 3
$44$:  44T2
$88$:  44T5

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: None

Low degree siblings

46T18

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 64 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $46552=2^{3} \cdot 11 \cdot 23^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.