Properties

Label 33T42
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 $t$:  $42$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,29,16,11,28,22,8,25,18,10,27,17,5,33,14)(2,30,21,3,31,15,6,23,19,4,32,20,9,26,12)(7,24,13), (1,30,9,27,8,26,4,33,10,28)(2,31)(3,32,6,24,7,25,11,29,5,23)(12,22,13,20,17)(14,18,21,15,16)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$5$:  $C_5$
$6$:  $S_3$
$10$:  $C_{10}$
$30$:  $S_3 \times C_5$
$55$:  $C_{11}:C_5$
$110$:  22T5
$330$:  33T7
$3630$:  33T20

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 11: None

Low degree siblings

33T42 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 98 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.