Properties

Label 21T28
Degree $21$
Order $1029$
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 $t$:  $28$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $7$
Generators:  (1,20,8,3,16,14,5,19,13,7,15,12,2,18,11,4,21,10,6,17,9), (1,7,6,5,4,3,2)(8,10,12,14,9,11,13)(15,18,21,17,20,16,19)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$3$:  $C_3$
$7$:  $C_7$
$21$:  $C_7:C_3$ x 2, $C_{21}$
$147$:  21T12, 21T13 x 2

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 7: None

Low degree siblings

21T28 x 11

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 133 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $1029=3 \cdot 7^{3}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  [1029, 15]
Character table: not available.