Properties

Label 22T43
Order \(8110080\)
n \(22\)
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)
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)
$|\Aut(F/K)|$:  $2$

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:  Data not available
Character table: Data not available.