Properties

Label 22T46
Order \(39916800\)
n \(22\)
Cyclic No
Abelian No
Solvable No
Primitive No
$p$-group No

Related objects

Learn more about

Group action invariants

Degree $n$ :  $22$
Transitive number $t$ :  $46$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,5,13,21,19,18,7,16,9,11,4)(2,6,14,22,20,17,8,15,10,12,3), (1,2)(3,4)(5,15,19,14,11,22,7,17,9,6,16,20,13,12,21,8,18,10)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
19958400:  $A_{11}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 11: $A_{11}$

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 62 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $39916800=2^{8} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.