Properties

Label 21T32
Degree $21$
Order $2058$
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 $t$:  $32$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $7$
Generators:  (1,18,12,3,16,10,5,21,8,7,19,13,2,17,11,4,15,9,6,20,14), (1,7,6,5,4,3,2)(8,19,13,17,11,15,9,20,14,18,12,16,10,21)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$6$:  $S_3$
$7$:  $C_7$
$14$:  $C_{14}$
$42$:  21T6
$294$:  14T15

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 7: None

Low degree siblings

21T32 x 5, 42T269 x 6, 42T281 x 3, 42T282 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 140 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.