Properties

Label 21T50
Degree $21$
Order $10206$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $21$
Transitive number $t$:  $50$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,7,14,21,4,11,18,3,8,13,20,6,12,17)(2,9,15,19,5,10,16), (1,13,6,17,9,19,10)(2,14,4,18,7,21,11)(3,15,5,16,8,20,12)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$7$:  $C_7$
$14$:  $C_{14}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 7: $C_7$

Low degree siblings

21T50 x 51, 42T554 x 52

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 66 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $10206=2 \cdot 3^{6} \cdot 7$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.