Properties

Label 22T43
Degree $22$
Order $8110080$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no

Related objects

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Group action invariants

Degree $n$:  $22$
Transitive number $t$:  $43$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,21,17,20)(2,22,18,19)(3,5,8,16,4,6,7,15)(9,10)(11,12)(13,14), (1,9,16,19,14,12,18,4,6,22,8)(2,10,15,20,13,11,17,3,5,21,7)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$7920$:  $M_{11}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 11: $M_{11}$

Low degree siblings

22T43, 44T554

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 52 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $8110080=2^{14} \cdot 3^{2} \cdot 5 \cdot 11$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.