Properties

Label 33T41
Degree $33$
Order $39930$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$5$:  $C_5$
$6$:  $C_6$
$10$:  $C_{10}$
$15$:  $C_{15}$
$30$:  $C_{30}$
$110$:  $F_{11}$
$330$:  33T8
$3630$:  33T19

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 11: None

Low degree siblings

33T41 x 39

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

There are 77 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $39930=2 \cdot 3 \cdot 5 \cdot 11^{3}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.