Properties

Label 46T11
Degree $46$
Order $11638$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$22$:  $D_{11}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: None

Low degree siblings

There are no siblings 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:  $11638=2 \cdot 11 \cdot 23^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.