Properties

Label 22T36
Degree $22$
Order $112640$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

Related objects

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Group action invariants

Degree $n$:  $22$
Transitive number $t$:  $36$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,15,5,10,4,2,16,6,9,3)(7,17,14,19,22,8,18,13,20,21)(11,12), (1,6,19,14,4)(2,5,20,13,3)(7,15,21,10,12,8,16,22,9,11)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$5$:  $C_5$
$10$:  $C_{10}$
$55$:  $C_{11}:C_5$
$110$:  22T5
$56320$:  22T33

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 11: $C_{11}:C_5$

Low degree siblings

22T36 x 2, 44T314 x 3, 44T315 x 3

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 80 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $112640=2^{11} \cdot 5 \cdot 11$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.