Properties

Label 22T52
Degree $22$
Order $40874803200$
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 $t$:  $52$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,14)(2,13)(3,9,16,8,19)(4,10,15,7,20)(5,18,6,17), (1,10,21,19,4,15,11)(2,9,22,20,3,16,12)(5,8,14,6,7,13)(17,18)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$19958400$:  $A_{11}$
$39916800$:  22T46
$20437401600$:  22T49

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 11: $A_{11}$

Low degree siblings

44T1750

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 400 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $40874803200=2^{18} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.