Properties

Label 33T48
Degree $33$
Order $79860$
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)
$|\Aut(F/K)|$:  $1$
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)

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:  not available
Character table: not available.