Properties

Label 22T48
Degree $22$
Order $125452800$
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 $t$:  $48$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,16,2,14,11,17,8,18,6,15,9,20)(3,22,10,19)(4,21,7,13,5,12), (1,16,6,19,9,20,11,17,5,14,8,22,4,13,3,12)(2,18)(7,15,10,21)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 11: None

Low degree siblings

24T24600, 44T1454

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 65 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $125452800=2^{9} \cdot 3^{4} \cdot 5^{2} \cdot 11^{2}$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.