Properties

Label 22T44
Degree $22$
Order $16220160$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no

Related objects

Learn more about

Group action invariants

Degree $n$:  $22$
Transitive number $t$:  $44$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,21,10,18,11,15,5,4,2,22,9,17,12,16,6,3)(7,8)(13,19)(14,20), (1,15,7,13,11,10,17,4,2,16,8,14,12,9,18,3)(5,19)(6,20)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$7920$:  $M_{11}$
$15840$:  22T26
$8110080$:  22T43

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 11: $M_{11}$

Low degree siblings

22T44, 44T613, 44T615 x 2, 44T617 x 2

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 104 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $16220160=2^{15} \cdot 3^{2} \cdot 5 \cdot 11$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.