Properties

Label 21T39
Degree $21$
Order $5103$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

Related objects

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Group action invariants

Degree $n$:  $21$
Transitive number $t$:  $39$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $3$
Generators:  (1,13,6,16,7,21,10)(2,14,4,17,8,20,11)(3,15,5,18,9,19,12), (1,15,4,16,8,19,12)(2,13,5,17,9,21,10)(3,14,6,18,7,20,11)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$7$:  $C_7$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 7: $C_7$

Low degree siblings

21T39 x 51

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

There are 111 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $5103=3^{6} \cdot 7$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  [5103, 4034]
Character table: not available.