Properties

Label 44T38
Degree $44$
Order $968$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$8$:  $D_{4}$
$22$:  $D_{11}$ x 2
$44$:  $D_{22}$ x 2
$484$:  22T9

Resolvents shown for degrees $\leq 29$

Subfields

Degree 2: $C_2$

Degree 4: $D_{4}$

Degree 11: None

Degree 22: 22T9

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 95 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, 20]
Character table: not available.