Properties

Label 33T50
Degree $33$
Order $99825$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $33$
Transitive number $t$:  $50$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,28,21,6,27,13,11,26,16,5,25,19,10,24,22,4,23,14,9,33,17,3,32,20,8,31,12,2,30,15,7,29,18), (1,12,32,2,16,29,3,20,26,4,13,23,5,17,31,6,21,28,7,14,25,8,18,33,9,22,30,10,15,27,11,19,24)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$3$:  $C_3$
$75$:  $C_5^2 : C_3$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 11: None

Low degree siblings

There are no siblings 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:  $99825=3 \cdot 5^{2} \cdot 11^{3}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.