Properties

Label 22T47
Degree $22$
Order $79833600$
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 $t$:  $47$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,13,20,22,18,7,4,16,10,11,6,2,14,19,21,17,8,3,15,9,12,5), (1,15,10,8,6,20,12)(2,16,9,7,5,19,11)(3,17,22,13)(4,18,21,14)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$39916800$:  $S_{11}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 11: $S_{11}$

Low degree siblings

22T47, 44T1258

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 112 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $79833600=2^{9} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.