Properties

Label 44T27
Order \(484\)
n \(44\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $C_{22}\times D_{11}$

Learn more about

Group action invariants

Degree $n$ :  $44$
Transitive number $t$ :  $27$
Group :  $C_{22}\times D_{11}$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,29,3,43,6,35,8,28,10,42,11,33,13,26,16,40,17,31,20,23,22,37)(2,30,4,44,5,36,7,27,9,41,12,34,14,25,15,39,18,32,19,24,21,38), (1,30,13,25,3,44,16,39,6,36,17,32,8,27,20,24,10,41,22,38,11,34)(2,29,14,26,4,43,15,40,5,35,18,31,7,28,19,23,9,42,21,37,12,33)
$|\Aut(F/K)|$:  $22$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
11:  $C_{11}$
22:  $D_{11}$, 22T1 x 3
44:  $D_{22}$
242:  22T7

Resolvents shown for degrees $\leq 29$

Subfields

Degree 2: $C_2$ x 3

Degree 4: $C_2^2$

Degree 11: None

Degree 22: 22T7

Low degree siblings

There are no siblings with degree $\leq 29$
Data on whether or not a number field with this Galois group has arithmetically equivalent fields has not been computed.

Conjugacy Classes

There are 154 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $484=2^{2} \cdot 11^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [484, 10]
Character table: Data not available.