Properties

Label 22T36
Order \(112640\)
n \(22\)
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)
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)
$|\Aut(F/K)|$:  $2$

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:  Data not available
Character table: Data not available.