Properties

Label 22T58
Order \(562000363888803840000\)
n \(22\)
Cyclic No
Abelian No
Solvable No
Primitive Yes
$p$-group No

Related objects

Learn more about

Group action invariants

Degree $n$ :  $22$
Transitive number $t$ :  $58$
Parity:  $1$
Primitive:  Yes
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,2,3), (1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

None

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 11: None

Low degree siblings

There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

There are 513 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $562000363888803840000=2^{18} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.