Properties

Label 33T43
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 $t$:  $43$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,22,31)(2,14,29,4,20,25,10,16,24,6,15,32,5,12,23)(3,17,27,7,18,30,8,21,28,11,19,33,9,13,26), (1,15,7,18,4,22,11,20,2,21)(3,16,6,12,10,14,8,13,9,19)(5,17)(24,30,28,25,26,33,27,29,32,31)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$5$:  $C_5$
$6$:  $S_3$
$10$:  $C_{10}$
$30$:  $S_3 \times C_5$
$110$:  $F_{11}$
$330$:  33T9
$3630$:  33T20

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 11: None

Low degree siblings

33T43 x 9

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 65 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.