Properties

Label 44T32
Order \(880\)
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 $t$ :  $32$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,33)(2,34)(3,36)(4,35)(5,30)(6,29)(7,32)(8,31)(9,27)(10,28)(11,25)(12,26)(13,21)(14,22)(15,23)(16,24)(17,18)(37,41)(38,42)(39,43)(40,44), (1,39,5,9,25,4,38,8,11,28)(2,40,6,10,26,3,37,7,12,27)(13,43,21,31,20,16,41,23,29,18)(14,44,22,32,19,15,42,24,30,17)(33,36)(34,35), (1,17,37,31,42,4,20,40,30,44,2,18,38,32,41,3,19,39,29,43)(5,36,13,23,11,8,34,16,22,9,6,35,14,24,12,7,33,15,21,10)(25,28,26,27)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 7
4:  $C_2^2$ x 7
5:  $C_5$
8:  $D_{4}$ x 2, $C_2^3$
10:  $C_{10}$ x 7
16:  $D_4\times C_2$
20:  20T3 x 7
40:  20T12 x 2
110:  $F_{11}$
220:  22T6 x 3

Resolvents shown for degrees $\leq 29$

Subfields

Degree 2: $C_2$

Degree 4: $D_{4}$

Degree 11: $F_{11}$

Degree 22: 22T6

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:  $880=2^{4} \cdot 5 \cdot 11$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [880, 118]
Character table: Data not available.