Properties

Label 22T37
Order \(225280\)
n \(22\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Related objects

Learn more about

Group action invariants

Degree $n$ :  $22$
Transitive number $t$ :  $37$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,3,14,19,6)(2,4,13,20,5)(7,11,9,21,16)(8,12,10,22,15)(17,18), (1,11,3,5,22,18,7,16,13,20)(2,12,4,6,21,17,8,15,14,19)(9,10)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
5:  $C_5$
10:  $C_{10}$ x 3
20:  20T3
110:  $F_{11}$
220:  22T6
112640:  22T34

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 11: $F_{11}$

Low degree siblings

22T37, 44T333, 44T336, 44T339 x 2, 44T340 x 2, 44T341

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 88 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $225280=2^{12} \cdot 5 \cdot 11$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.