Properties

Label 22T29
Order \(22528\)
n \(22\)
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 $t$ :  $29$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,13,4,16,6,17,8,19,9,22,11)(2,14,3,15,5,18,7,20,10,21,12), (1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16,8,15)(9,13)(10,14)
$|\Aut(F/K)|$:  $2$

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 30, 22T30 x 31, 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:  Data not available
Character table: Data not available.