Properties

Label 44T33
Degree $44$
Order $968$
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)
$|\Aut(F/K)|$:  $22$
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)

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: not available.