Properties

Label 44T5
Order \(88\)
n \(44\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $C_{11}\times D_4$

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Group action invariants

Degree $n$ :  $44$
Transitive number $t$ :  $5$
Group :  $C_{11}\times D_4$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $2$
Generators:  (1,36,25,15,6,40,30,19,10,44,33,23,14,3,38,27,18,8,42,32,21,12,2,35,26,16,5,39,29,20,9,43,34,24,13,4,37,28,17,7,41,31,22,11), (1,44,41,40,37,36,34,31,29,28,26,24,21,20,18,16,14,12,10,8,6,3)(2,43,42,39,38,35,33,32,30,27,25,23,22,19,17,15,13,11,9,7,5,4)
$|\Aut(F/K)|$:  $22$

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:  22T1 x 3

Resolvents shown for degrees $\leq 29$

Subfields

Degree 2: $C_2$

Degree 4: $D_{4}$

Degree 11: $C_{11}$

Degree 22: 22T1

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 55 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $88=2^{3} \cdot 11$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [88, 9]
Character table: Data not available.