Properties

Label 21T30
Degree $21$
Order $2058$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $21$
Transitive number $t$:  $30$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,15,5,19,2,16,6,20,3,17,7,21,4,18)(8,14)(9,13)(10,12), (1,12,2,13,3,14,4,8,5,9,6,10,7,11)(15,21)(16,20)(17,19)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$6$:  $S_3$
$14$:  $D_{7}$
$42$:  $D_{21}$
$294$:  14T15

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 7: None

Low degree siblings

21T30 x 5, 42T267 x 6, 42T280 x 3, 42T283 x 2

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 77 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $2058=2 \cdot 3 \cdot 7^{3}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.