Properties

Label 22T7
Degree $22$
Order $242$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{11}\times D_{11}$

Related objects

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$11$:  $C_{11}$
$22$:  $D_{11}$, 22T1

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 11: None

Low degree siblings

22T7 x 4

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 77 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $242=2 \cdot 11^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  [242, 3]
Character table: not available.