Properties

Label 44T49
Order \(1936\)
n \(44\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Learn more about

Group action invariants

Degree $n$ :  $44$
Transitive number $t$ :  $49$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,24,7,31,14,39,20,25,3,34,9,41,15,27,22,36,5,44,12,29,17,38,2,23,8,32,13,40,19,26,4,33,10,42,16,28,21,35,6,43,11,30,18,37), (1,36,3,23,5,33,8,43,10,31,11,41,14,29,15,40,17,28,19,37,21,25)(2,35,4,24,6,34,7,44,9,32,12,42,13,30,16,39,18,27,20,38,22,26), (1,26,6,28,10,30,13,31,17,34,22,36,3,38,7,40,11,42,16,43,19,24,2,25,5,27,9,29,14,32,18,33,21,35,4,37,8,39,12,41,15,44,20,23)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 7
4:  $C_2^2$ x 7
8:  $D_{4}$ x 2, $C_2^3$
16:  $D_4\times C_2$
22:  $D_{11}$ x 2
44:  $D_{22}$ x 6
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 160 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $1936=2^{4} \cdot 11^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [1936, 134]
Character table: Data not available.