Properties

Label 22T30
Degree $22$
Order $22528$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

Related objects

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Group action invariants

Degree $n$:  $22$
Transitive number $t$:  $30$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,22,19,17,15,14,11,10,7,6,4)(2,21,20,18,16,13,12,9,8,5,3), (1,9)(2,10)(3,7)(4,8)(11,22,12,21)(13,20)(14,19)(15,17,16,18)

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: None

Degree 11: $D_{11}$

Low degree siblings

22T29 x 31, 22T30 x 30, 44T147 x 31, 44T148 x 31, 44T204 x 155, 44T205 x 155, 44T206 x 155, 44T207 x 31, 44T208 x 155, 44T209 x 155, 44T210 x 155, 44T211 x 155

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 100 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $22528=2^{11} \cdot 11$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.