Properties

Label 22T52
Order \(40874803200\)
n \(22\)
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)
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)
$|\Aut(F/K)|$:  $2$

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:  Data not available
Character table: Data not available.