Properties

Label 33T48
Order \(79860\)
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 $t$ :  $48$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,2,6,11,9)(3,10,5,7,4)(12,33,17,25,20,29,13,27,22,28)(14,32,16,31,15,26,21,23,18,30)(19,24), (1,25,20)(2,27,18,3,29,16,5,33,12,9,30,15,6,24,21,11,23,22,10,32,13,8,28,17,4,31,14,7,26,19)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
5:  $C_5$
6:  $S_3$
10:  $C_{10}$ x 3
12:  $D_{6}$
20:  20T3
30:  $S_3 \times C_5$
60:  30T12
110:  $F_{11}$
220:  22T6
660:  33T11
7260:  33T25

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 11: None

Low degree siblings

33T48 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 73 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $79860=2^{2} \cdot 3 \cdot 5 \cdot 11^{3}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.