Properties

Label 33T32
Order \(15972\)
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 $t$ :  $32$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,31,9,27,6,23,3,30,11,26,8,33,5,29,2,25,10,32,7,28,4,24)(12,15,18,21,13,16,19,22,14,17,20), (1,2)(3,11)(4,10)(5,9)(6,8)(12,24,17,26,22,28,16,30,21,32,15,23,20,25,14,27,19,29,13,31,18,33)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
6:  $S_3$
12:  $D_{6}$
22:  $D_{11}$
44:  $D_{22}$
132:  33T5
1452:  33T15

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 11: None

Low degree siblings

33T32 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 221 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $15972=2^{2} \cdot 3 \cdot 11^{3}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.