Properties

Label 22T23
Degree $22$
Order $11264$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

Related objects

Learn more about

Group action invariants

Degree $n$:  $22$
Transitive number $t$:  $23$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,11,21,10,19,8,18,6,15,3,14)(2,12,22,9,20,7,17,5,16,4,13), (1,4,6,8,10,12,14,15,17,20,21)(2,3,5,7,9,11,13,16,18,19,22)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$11$:  $C_{11}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 11: $C_{11}$

Low degree siblings

22T23 x 92, 44T116 x 31, 44T117 x 465, 44T118 x 465, 44T119 x 465, 44T120 x 465, 44T121 x 930, 44T122 x 930, 44T123 x 930, 44T124 x 930, 44T125 x 930, 44T126 x 930, 44T127 x 930, 44T128 x 930, 44T129 x 930, 44T130 x 930, 44T131 x 930, 44T132 x 930, 44T133 x 930, 44T134 x 930, 44T135 x 930

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:  $11264=2^{10} \cdot 11$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.