Properties

Label 44T34
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 $t$:  $34$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,25,19,28)(2,26,20,27)(3,35,17,39)(4,36,18,40)(5,24,15,30)(6,23,16,29)(7,33,14,42)(8,34,13,41)(9,43,11,31)(10,44,12,32)(21,37,22,38), (1,21,20,17,15,14,12,10,7,5,3,2,22,19,18,16,13,11,9,8,6,4)(23,44,41,39,38,36,33,31,30,28,25,24,43,42,40,37,35,34,32,29,27,26)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_4$ x 2, $C_2^2$
$8$:  $C_4\times C_2$
$484$:  22T8

Resolvents shown for degrees $\leq 29$

Subfields

Degree 2: $C_2$

Degree 4: $C_4$

Degree 11: None

Degree 22: 22T8

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 68 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, 38]
Character table: not available.