Properties

Label 46T10
Degree $46$
Order $4232$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$8$:  $D_{4}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: None

Low degree siblings

46T10

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 104 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $4232=2^{3} \cdot 23^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.