Properties

Label 44T37
Order \(968\)
n \(44\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 7
4:  $C_2^2$ x 7
8:  $C_2^3$
22:  $D_{11}$ x 2
44:  $D_{22}$ x 6
484:  22T9

Resolvents shown for degrees $\leq 29$

Subfields

Degree 2: $C_2$ x 3

Degree 4: $C_2^2$

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 98 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, 39]
Character table: Data not available.