Properties

Label 21T40
Degree $21$
Order $6174$
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 $t$:  $40$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,6,2)(4,5,7)(8,21,11,20,9,16)(10,18,12,15,13,17)(14,19), (1,19,8,2,15,11,3,18,14,4,21,10,5,17,13,6,20,9,7,16,12)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$6$:  $S_3$, $C_6$
$18$:  $S_3\times C_3$
$21$:  $C_7:C_3$
$42$:  $(C_7:C_3) \times C_2$
$126$:  21T11
$882$:  14T26

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 7: None

Low degree siblings

21T40 x 5, 42T464 x 6, 42T473 x 3, 42T474 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 60 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $6174=2 \cdot 3^{2} \cdot 7^{3}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.