Properties

Label 44T32
Degree $44$
Order $880$
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)
$|\Aut(F/K)|$:  $2$
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)

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: not available.