Properties

Label 22T32
Order \(45056\)
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 $t$ :  $32$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,6)(2,5)(7,22)(8,21)(9,20,10,19)(11,17)(12,18)(13,16)(14,15), (1,4)(2,3)(5,21)(6,22)(7,19,8,20)(9,18,10,17)(11,16,12,15)(13,14)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
22:  $D_{11}$
44:  $D_{22}$
22528:  22T29

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 11: $D_{11}$

Low degree siblings

22T32 x 61, 44T236 x 31, 44T239 x 31, 44T240 x 62, 44T241 x 62, 44T266 x 310, 44T267 x 310, 44T268 x 310, 44T269 x 31, 44T270 x 155, 44T271 x 155, 44T272 x 155, 44T273 x 310, 44T274 x 310, 44T275 x 310

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 200 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $45056=2^{12} \cdot 11$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.