Properties

Label 22T32
Degree $22$
Order $45056$
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)
$|\Aut(F/K)|$:  $2$
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)

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:  not available
Character table: not available.