Properties

Label 33T43
Order \(39930\)
n \(33\)
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)
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)
$|\Aut(F/K)|$:  $1$

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:  Data not available
Character table: Data not available.