Properties

Label 22T49
Degree $22$
Order $20437401600$
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 $t$:  $49$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,16,13,6,3,10,22)(2,15,14,5,4,9,21)(7,11)(8,12)(17,20)(18,19), (1,17,3,10,12,6,7,2,18,4,9,11,5,8)(13,19,15)(14,20,16)(21,22)

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

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 200 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $20437401600=2^{17} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.