Properties

Label 44T33
Order \(968\)
n \(44\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Learn more about

Group action invariants

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

Low degree resolvents

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

Resolvents shown for degrees $\leq 29$

Subfields

Degree 2: $C_2$

Degree 4: $D_{4}$

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 275 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $968=2^{3} \cdot 11^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [968, 26]
Character table: Data not available.